{"id":12712,"date":"2021-04-01T21:43:30","date_gmt":"2021-04-01T16:13:30","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=12712"},"modified":"2021-08-21T20:29:05","modified_gmt":"2021-08-21T14:59:05","slug":"04-06-00","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/04-06-00\/","title":{"rendered":"04.06.00 &#8211; \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0d9a\u0dd2\u0db1\u0dca \u0dba\u0da7\u0dc0\u0dd6 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc4\u0dcf \u0d9d\u0db1 \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0d9a \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0"},"content":{"rendered":"\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?id=1Xfd74wulLDsyEulFDtQfKsXzLBEPrVG4&amp;export=download\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<h2 class=\"wp-block-heading\"><strong>\u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0d9a\u0dd2\u0db1\u0dca \u0dba\u0da7 \u0dc0\u0dd6 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba<\/strong><\/h2>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">y=f\\left(x\\right)<\/span> \u0dc3\u0d82\u0dad\u0dad\u0dd2\u0d9a \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0dc3\u0dbd\u0d9a\u0db8\u0dd4.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0db8\u0dd9\u0db8 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0dda \u0daf\u0dc5 \u0db4\u0dca\u200d\u0dbb\u0dc3\u0dca\u0dad\u0dcf\u0dbb\u0dba \u0dc3\u0dbd\u0d9a\u0dcf \u0db6\u0dbd\u0db8\u0dd4.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/PhigfgDXOxxnJfQAb0Bsur9s-qmpUJKxBpuPrUTfOVgOciuZJYuCKmenIO6NCXoF73hFD1Ubinoyk_tAJso4SYYZ5FSZBOFQhQkqmdsHc0jD_KWinckhjtwBk8P4EzvCRDfsdYY\" width=\"498\" height=\"329\" \/><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>PQRS \u0dc3\u0dd2\u0dc4\u0dd2\u0db1\u0dca \u0dad\u0dd3\u0dbb\u0dd4\u0dc0\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">\\delta A<\/span> \u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\delta A\\approx y.\\delta x<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\delta A}{\\delta x}\\approx y<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{\\delta x\\rightarrow0}\\frac{\\delta A}{\\delta x}=\\lim_{\\delta x\\rightarrow0}y<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\operatorname dA}{\\operatorname dx}=y<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\int dA=\\int y\\;dx<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}y&amp;=&amp;f\\left(x\\right),x=a,x=b,y=0\\end{array}<\/span> \u0dc0\u0d9a\u0dca\u200d\u0dbb \u0dc0\u0dbd\u0dd2\u0db1\u0dca \u0d86\u0dc0\u0dd8\u0dad \u0db4\u0dd9\u0daf\u0dd9\u0dc3\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">\\delta A<\/span> \u0db1\u0db8\u0dca,<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\boxed{\\begin{array}{rcl}A&amp;=&amp;\\int_a^by\\operatorname dx\\end{array}}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0db1\u0dd2\u0dc1\u0dca\u0da0\u0dd2\u0dad \u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0dbd\u0db6\u0dcf \u0d9c\u0db1\u0dca\u0db1\u0dcf \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0d85\u0d9a\u0dca\u0dc2\u0dba\u0da7 \u0d89\u0dc4\u0dc5\u0dd2\u0db1\u0dca \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dba\u0dd2 \u0db1\u0db8\u0dca \u0db0\u0db1 \u0dbd\u0dd9\u0dc3\u0dad\u0dca \u0d85\u0d9a\u0dca\u0dc2\u0dba\u0da7 \u0db4\u0dc4\u0dc5\u0dd2\u0db1\u0dca \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dba\u0dd2 \u0db1\u0db8\u0dca \u0d8d\u0dab \u0dbd\u0dd9\u0dc3\u0dad\u0dca \u0dbd\u0dd0\u0db6\u0dda \u0db1\u0db8\u0dd4\u0dad\u0dca \u0dba\u0db8\u0dca \u0db4\u0dca\u200d\u0dbb\u0dcf\u0db1\u0dca\u0dad\u0dbb\u0dba\u0d9a\u0dca \u0dad\u0dd4\u0dc5 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0d89\u0daf\u0dd2\u0dbb\u0dd2\u0db4\u0dad\u0dca \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dda\u0daf\u0dd3 \u0d91\u0dba \u0db0\u0db1 \u0d85\u0d9c\u0dba\u0d9a\u0dca \u0dbd\u0dd9\u0dc3 \u0dbd\u0db6\u0dcf \u0daf\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4 \u0db1\u0dd2\u0dc3\u0dcf \u0d85\u0dc0\u0dc3\u0db1\u0dca \u0d85\u0d9c\u0dba\u0dd9\u0dc4\u0dd2 \u0dc0\u0dd2\u0dc1\u0dcf\u0dbd\u0dad\u0dca\u0dc0\u0dba \u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb \u0d89\u0daf\u0dd2\u0dbb\u0dd2\u0db4\u0dad\u0dca \u0d9a\u0dc5 \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/p>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n\r\n\r\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/fQPbMhprIhJujheGepOt9ByeEHO91a30U9lDY2fhNEGaOBWtgbclYi9Om3dm7UhjJVKbfE2__7MOUrYpXVhNH8eIfvLfq-RdUtP0qwt_TQqBtry9QCMrd7ttrgJ0zZYyuok7Gmg\" width=\"649\" height=\"260\" \/><\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}A&amp;=&amp;\\int_a^bf\\left(x\\right)\\operatorname dx\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;A=-\\int_a^b{f\\left(x\\right)}\\operatorname dx\\end{array}<\/span>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 34px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n\r\n\r\n<p>\u0db8\u0dd9\u0db8 \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf \u0daf\u0dd9\u0d9a\u0da7\u0db8 \u0db4\u0ddc\u0daf\u0dd4\u0dc0\u0dda \u0d9c\u0dad\u0dca \u0dc0\u0dd2\u0da7,<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\left|A=\\int_a^bf\\left(x\\right)\\operatorname dx\\right|\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n\r\n\r\n<p><span class=\"has-inline-color\" style=\"color: #ff0000\"><strong>\u0d9c\u0dd0\u0da7\u0dc5\u0dd4 \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8\u0dda\u0daf\u0dd3 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0db0\u0db1 \u0dc4\u0dcf \u0d8d\u0dab \u0dc0\u0db1 \u0db4\u0dca\u200d\u0dbb\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0daf\u0dd9\u0d9a\u0db8 \u0d91\u0d9a\u0db8 \u0db4\u0dca\u200d\u0dbb\u0dc3\u0dca\u0dae\u0dcf\u0dbb\u0dba\u0d9a \u0dbd\u0dd0\u0db6\u0dd2\u0dba \u0dc4\u0dd0\u0d9a\u0dd2 \u0db1\u0dd2\u0dc3\u0dcf \u0dc3\u0dd1\u0db8\u0dc0\u0dd2\u0da7\u0db8 \u0d85\u0daf\u0dcf\u0dc5 \u0db4\u0dca\u200d\u0dbb\u0dcf\u0db1\u0dca\u0dad\u0dbb\u0dba \u0dad\u0dd4\u0dc5 \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba \u0d87\u0db3\u0dd3\u0db8 \u0dc3\u0dd2\u0daf\u0dd4\u0d9a\u0ddc\u0da7 \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0 \u0dc0\u0dd2\u0dc3\u0db3\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/strong><\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u0d8b\u0daf\u0dcf: <\/strong>(1.)<strong> <span class=\"wp-katex-eq\" data-display=\"false\">y=x^2<\/span>\u00a0\u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0dd9\u0db1\u0dd4\u0dad\u0dca<span class=\"wp-katex-eq\" data-display=\"false\"> x=1,x=2 <\/span> \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dbd\u0dd2\u0db1\u0dd4\u0dad\u0dca \u0d86\u0dc0\u0dd8\u0dad \u0dc0\u0dd6 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-left\"><strong><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/liBvfe4Kc2dmsDSff1M0Xai-2-CWAWtcoUzth8NlF3OHkVOlUESB8ZoIVtqn7i0sbSiINjxKEjBPoqnTUMe5tG1_kTzj2YwaQyHCsMN5BBuuc7_jB4FiRuI2A6_QoYqIDVX7cuY\" width=\"383\" height=\"371\" \/><\/strong><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">S=\\int_1^2y\\;dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">S=\\int_1^2x^2\\;dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">S={\\left[\\frac{x^3}3\\right]^2}_1<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">S=\\frac13\\left[2^3-1^3\\right]=\\frac73\\text{\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u00a0\u0d92\u0d9a\u0d9a}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>y=x<sup>3<\/sup>-6x<sup>2<\/sup>+8x \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0dad\u0dca, x-\u0d85\u0d9a\u0dca\u0dc2\u0dba\u0dad\u0dca \u0d85\u0dad\u0dbb \u0dc0\u0dd6 \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u0db8\u0dd9\u0dc4\u0dd2\u0daf\u0dd3 \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dbd\u0dd9\u0dc3 \u0dc4\u0db3\u0dd4\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1\u0dda \u0db8\u0dd0\u0db1\u0d9c\u0dad \u0dc4\u0dd0\u0d9a\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba\u0db1\u0dca\u0dba. \u0d91\u0db8 \u0db1\u0dd2\u0dc3\u0dcf \u0db4\u0dc4\u0dad \u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 a \u0dc4\u0dcf b \u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba\u0db1\u0dca \u0d91\u0d9a\u0dad\u0dd4 \u0d9a\u0dc5 \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2. \u0db8\u0dd9\u0dba \u0db0\u0db1 \u0dc4\u0dcf \u0d8d\u0dab \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd \u0dbd\u0dd9\u0dc3 \u0dbd\u0dd0\u0db6\u0dd3\u0db8 \u0db1\u0dd2\u0dc3\u0dcf \u0d91\u0d9a\u0dc0\u0dbb \u0dc3\u0dd3\u0db8\u0dcf\u0dc0\u0db1\u0dca\u0dc4\u0dd2 \u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca \u0dbd\u0db6\u0dcf \u0d9c\u0dad \u0db1\u0ddc\u0dc4\u0dd0\u0d9a\u0dd2\u0dba. \u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf \u0db0\u0db1 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd \u0dc4\u0dcf \u0d8d\u0dab \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd \u0dc0\u0dd9\u0db1 \u0dc0\u0dd9\u0db1\u0db8 \u0d9c\u0dab\u0db1\u0dba \u0d9a\u0dbb \u0dbd\u0db6\u0dcf \u0d9c\u0dad \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.\u00a0<\/p>\r\n\r\n\r\n\r\n<p>y=x<sup>3<\/sup>-6x<sup>2<\/sup>+8x<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 = x(x-2)(x-4)<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/Qz_gxYx7eio_-22hC2dE6_rSpDXnwFOdeShv305Ksk1RkUSv6pD_7YaedFvHf5OaMxqTsT_3dh1_AQ4A8laT5XXx5XVmAEzcUnwqKYRj8cVncSxmZZp6ZiYtcdu3-P60hRY55PI\" width=\"480\" height=\"407\" \/><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">a\\;\\text{\u0dc4\u0dd2\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}=\\int_0^2(x^3-6x^2+8x)\\;dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">a\\;\\text{\u0dc4\u0dd2\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}={\\left[\\frac14x^4-2x^3+4x^2\\right]^2}_0<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">a\\;\\text{\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}=\\left[\\frac14.2^4-2.2^3+4.2^2\\right]\\;-\\left[0-0+0\\right]<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">a\\;\\text{\u0dc4\u0dd2\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}=4\\;\\text{\u0dc0\u0dbb\u0dca\u0d9c\u00a0\u0d92\u0d9a\u0d9a}<\/span><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 37px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">b\\;\\text{\u0dc4\u0dd2\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}=-\\int_2^4(x^3-6x^2+8x)\\;dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">b\\;\\text{\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}=-\\;{\\left[\\frac14x^4-2x^3+4x^2\\right]^4}_2<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">b\\;\\text{\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}=\\;-\\;\\left\\{\\left[\\frac14.4^4-2.4^3+4.4^2\\right]\\;-\\left[\\left[\\frac14.2^4-2.2^3+4.2^2\\right]\\right]\\right\\}<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">b\\;\\text{\u0dc4\u0dd2\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}=4\\;\\text{\u0dc0\u0dbb\u0dca\u0d9c\u00a0\u0d92\u0d9a\u0d9a}<\/span><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 25px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><strong>\u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0db8\u0dd4\u0dbd\u0dd4 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba<\/strong>= <em>a<\/em> \u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba + <em>b<\/em> \u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><strong>\u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0db8\u0dd4\u0dbd\u0dd4 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba<\/strong>=<em> 4 <\/em>+<em> 4<\/em> =<em>8<\/em> \u0dc0\u0dbb\u0dca\u0d9c \u0d92\u0d9a\u0d9a<\/p>\r\n\r\n\r\n\r\n<h3 class=\"wp-block-heading\"><strong>\u0dc0\u0d9a\u0dca\u200d\u0dbb \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0d86\u0dc0\u0dd8\u0dad \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc3\u0dd9\u0dc0\u0dd3\u0db8<\/strong><\/h3>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/5JUZJLAwh49ZzaGDrZj0WZWdvTU1ZBzPKyv6BZv-ekBnsPWA4Z8Fb1yLiiGMCgppKPMgSveJ4FOkkJv_g10DZ2p-IfgbjpIpba9F2Fjq2Jf3igIJH58am22E5UIaCI1nMbm_ZHg\" width=\"650\" height=\"452\" \/><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">\u0d85\u0db3\u0dd4\u0dbb\u0dd4 \u0d9a\u0ddc\u0da7\u0dc3\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba = {f(x) , x- \u0d85\u0d9a\u0dca\u0dc2\u0dba\u0dad\u0dca \u0d85\u0dad\u0dbb \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba} \u2013{ g(x), x- \u0d85\u0d9a\u0dca\u0dc2\u0dba\u0dad\u0dca \u0d85\u0dad\u0dbb \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{\u0d85\u0db3\u0dd4\u0dbb\u0dd4\u00a0\u0d9a\u0ddc\u0da7\u0dc3\u0dda\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba\u00a0}\\;=\\int_a^bf\\left(x\\right)\\;dx\\;-\\int_a^bg\\left(x\\right)\\;dx\\;<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{\u0d85\u0db3\u0dd4\u0dbb\u0dd4\u00a0\u0d9a\u0ddc\u0da7\u0dc3\u0dda\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba\u00a0}\\;=\\int_a^b\\left\\{f\\left(x\\right)-g\\left(x\\right)\\right\\}\\;dx\\;<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>01. y=x<sup>3<\/sup> \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0dad\u0dca y=2x \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dad\u0dca \u0d85\u0dad\u0dbb \u0dc0\u0dd6 \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u0db8\u0dd9\u0dc4\u0dd2\u0daf\u0dd3 \u0db4\u0dc5\u0db8\u0dd4\u0dc0\u0dd9\u0db1\u0dca\u0db8 \u0db4\u0dca\u200d\u0dbb\u0dc3\u0dca\u0dad\u0dcf\u0dbb \u0daf\u0dd9\u0d9a\u0db8 \u0d91\u0d9a\u0db8 \u0d85\u0d9a\u0dca\u0dc2 \u0dba\u0dd4\u0d9c\u0dbd\u0dba\u0d9a\u0dca \u0db8\u0dad \u0d87\u0db3 \u0d91\u0dc0\u0dcf\u0dba\u0dda \u0da1\u0dda\u0daf\u0db1 \u0dbd\u0d9a\u0dca\u0dc2 \u0dc3\u0dbd\u0d9a\u0dd4\u0dab\u0dd4 \u0d9a\u0dc5 \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/p>\r\n\r\n\r\n\r\n<p>\u0da1\u0dda\u0daf\u0db1 \u0dbd\u0d9a\u0dca\u0dc2\u0dc0\u0dbd\u0daf\u0dd3,\u00a0\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">x<sup>3<\/sup>=2x<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">x(x<sup>2<\/sup>-2)=0<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">x(x-\u221a2)(x+\u221a2)=0<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">x=0, x=-\u221a2 \u0dc4\u0ddd x=\u221a2 \u0dc0\u0dda<\/p>\r\n\r\n\r\n\r\n<p>\u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf \u0da1\u0dda\u0daf\u0db1 \u0dbd\u0d9a\u0dca\u0dc2,<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">(\u221a2,2\u221a2) \u0dc4\u0dcf (-\u221a2,-2\u221a2)<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/rbjVfpOvuup7d6QhHr00Ij3vtYIJYJV8VnhsV9j2yRqC52AH1e8oJKVgFht7IdxFPXp-0bESlO7ay5IO-kvbVsB8dQntfguNxyQmDsp8yMpICpgImaYtLVBvdAn-Cjg-NbGtsIw\" width=\"536\" height=\"367\" \/><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">R_1\\;\\text{\u0dc4\u0dd2\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}\\;=\\;\\int_{-\\sqrt2}^0\\;(x^3-2x)\\;dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">R_1\\;\\text{\u0dc4\u0dd2\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}\\;=\\;{\\left[\\frac14x^4-x^2\\right]^0}_{-\\sqrt2}<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">R_1\\;\\text{\u0dc4\u0dd2\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}\\;=\\left[0-0\\right]\\;-\\;\\left[\\frac14\\left(-\\sqrt2\\right)^4-(-\\sqrt2)^2\\right]<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">R_1\\;\\text{\u0dc4\u0dd2\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}\\;=\\;1\\text{\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u00a0\u0d92\u0d9a\u0d9a}<\/span><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 17px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">R_{2\\;}\\text{\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba\u00a0}\\;=\\int_0^{\\left(2\\right)^\\frac12}(2x-x^3)\\;dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">R_2\\;\\text{\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}\\;=\\;{\\left[x^2-\\frac14x^4\\right]}_0^{-\\sqrt2}<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">R_2\\;\\text{\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}\\;=\\;\\left[\\frac14\\left(\\sqrt2\\right)^4-(\\sqrt2)^2\\right]\\;-\\;\\left[0-0\\right]\\;<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">R_2\\;\\text{\u0dc4\u0dd2\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba}\\;=\\;1\\text{\u00a0\u0dc0\u0dbb\u0dca\u0d9c\u00a0\u0d92\u0d9a\u0d9a}<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">\u0db8\u0dd4\u0dc5\u0dd4 \u0d9a\u0dca\u0dc2\u0dda\u0dad\u0dca\u200d\u0dbb\u0db5\u0dbd\u0dba=R<sub>1<\/sub> \u0d9a\u0dca\u0dc2\u0dda\u0dad\u0dca\u200d\u0dbb\u0db5\u0dbd\u0dba+R<sub>2<\/sub> \u0d9a\u0dca\u0dc2\u0dda\u0dad\u0dca\u200d\u0dbb\u0db5\u0dbd\u0dba<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">\u0db8\u0dd4\u0dc5\u0dd4 \u0d9a\u0dca\u0dc2\u0dda\u0dad\u0dca\u200d\u0dbb\u0db5\u0dbd\u0dba=1+1= 2 \u0dc0\u0dbb\u0dca\u0d9c \u0d92\u0d9a\u0d9a<\/p>\r\n\r\n\r\n\r\n<p><strong>2.y=6x-x<sup>2 <\/sup><\/strong><sup>\u00a0<\/sup><strong>\u0dc4\u0dcf<\/strong><strong> y=x<sup>2<\/sup>-4x<\/strong> <strong>\u0dba\u0db1 \u0dc0\u0d9a\u0dca\u200d\u0dbb \u0daf\u0dd9\u0d9a\u0dda \u0dc3\u0dd3\u0db8\u0dcf\u0dc0\u0db1 \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u0db4\u0dca\u200d\u0dbb\u0dc3\u0dca\u0dad\u0dcf\u0dbb\u0dba \u0d87\u0db3\u0dd3\u0db8 \u0dc3\u0db3\u0dc4\u0dcf \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc3\u0dcf\u0db0\u0d9a \u0dc0\u0dbd\u0da7 \u0dc0\u0dd9\u0db1\u0dca \u0d9a\u0dd2\u0dbb\u0dd3\u0db8 \u0dc4\u0dcf \u0dc0\u0dbb\u0dca\u0d9c \u0db4\u0dd6\u0dbb\u0dca\u0dab\u0dba \u0dba\u0db1 \u0daf\u0dd9\u0d9a\u0db8 \u0d9a\u0dc5 \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-left\">y=6x-x<sup>2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/sup><sub>\u00ad\u00ad\u00ad\u00ad<\/sub>y=x<sup>2<\/sup>-2x<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-left\">y<strong>\u00a0<\/strong>=9-(x-3)<sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0y=(x-1)<sup>2<\/sup>-1<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-left\">y=x(6-x)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 y=x(x-2)<\/p>\r\n\r\n\r\n\r\n<p>\u0da1\u0dda\u0daf\u0db1 \u0dbd\u0d9a\u0dca\u0dc2\u0dc0\u0dbd\u0daf\u0dd3,<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">6x-x<sup>2<\/sup>=x<sup>2<\/sup>-2x<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">2x<sup>2<\/sup> &#8211; 8x=0<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">x(x-4)=0<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-left\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n<p>x=0 <strong>\u00a0<\/strong>\u0dc4\u0dcf x=4 \u0da1\u0dda\u0daf\u0db1 \u0dbd\u0d9a\u0dca\u0dc2 \u0dc0\u0dbdx \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a \u0dc0\u0dda<strong>.<\/strong> \u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf \u0da1\u0dda\u0daf\u0db1 \u0dbd\u0d9a\u0dca\u0dc2(0,0) \u0dc4\u0dcf (4,8) \u0dc0\u0dda<strong>.<\/strong><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/T1I84WgJ8rvyGF7cqinlh6FZ_O2f3aa8JOMTcqtAZAAf1OLqCGhcMOb0WWZROMZT2MxuL6a6W6QXEjXyc7j4nz3rGObpBvwjgyF1jRV9G1WNEBkNDMEGelXsqGb2j84lcDtm3H0\" width=\"578\" height=\"393\" \/><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">\u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba = <span class=\"wp-katex-eq\" data-display=\"false\">\\int_0^4\\left\\{(6x-x^2)-(x^2-2x)\\right\\}\\;dx\\;<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">\u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba = <span class=\"wp-katex-eq\" data-display=\"false\">\\int_0^4\\left(8x-2x^2\\right)\\;dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">\u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba = <span class=\"wp-katex-eq\" data-display=\"false\">{\\left[4x^2-\\frac23x^3\\right]^4}_0<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">\u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba = <span class=\"wp-katex-eq\" data-display=\"false\">{\\left[4.4^2-\\frac23.4^3\\right]^4}_0\\;-\\left[0-0\\right]<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\">\u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba = <span class=\"wp-katex-eq\" data-display=\"false\">\\frac{64}3\\;\\text{\u0dc0\u0dbb\u0dca\u0d9c\u00a0\u0d92\u0d9a\u0d9a}<\/span><\/p>\r\n\r\n\r\n\r\n<h2 class=\"wp-block-heading\"><strong>\u0db4\u0dbb\u0dd2\u0db7\u0dca\u200d\u0dbb\u0db8\u0dab \u0db4\u0dbb\u0dd2\u0db8\u0dcf<\/strong><\/h2>\r\n\r\n\r\n\r\n<p><em><strong>\u00a0<\/strong>y= f(x)<\/em> \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba \u0dc4\u0dcf <em>y=0<\/em><strong>\u00a0<\/strong>\u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0d86\u0dc0\u0dd8\u0dad \u0db4\u0dd9\u0daf\u0dd9\u0dc3 <span class=\"wp-katex-eq\" data-display=\"false\">\\;2\\pi\\;rad\\;<\/span> <strong>\u00a0<\/strong>\u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0dd2\u0db1\u0dca <em>x<\/em><strong>\u00a0<\/strong>\u0d85\u0d9a\u0dca\u0dc2\u0dba \u0dc0\u0da7\u0dcf \u0db7\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba \u0d9a\u0dbd\u0dc0\u0dd2\u0da7 \u0da2\u0db1\u0db1\u0dba \u0dc0\u0db1 \u0d9d\u0db1 \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 \u0dc3\u0dd9\u0dc0\u0dd3\u0db8<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><strong><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/8AF_ndCxY16S1Arc6_WFJZuIpv5AABzqAZNrjGfxSuuSoyFcpsDwt6brhVeqLVjQu6i0Mka2tHILasK8_JDenSSgKvXjOTEqcD5o5G51dZg9Ic0kedZ7dBK3B6CChxbNVg6Jnok\" width=\"581\" height=\"494\" \/><\/strong><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\delta V\\approx\\pi y^2.\\delta x<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\delta V}{\\delta x}\\approx\\pi y^2<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{\\delta x\\rightarrow0}\\frac{\\delta V}{\\delta x}=\\lim_{\\delta x\\rightarrow0}\\pi y^2<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\operatorname dV}{\\operatorname dx}=\\pi y^2<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\int\\;dV\\;=\\pi\\int\\;y^{2\\;}dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\boxed{V\\;=\\pi\\int\\;y^{2\\;}dx}<\/span><\/p>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><em>y=f(x),x=a,x=b,y=0<\/em> \u00a0\u0dc0\u0d9a\u0dca\u200d\u0dbb \u0dc0\u0dbd\u0dd2\u0db1\u0dca \u0d86\u0dc0\u0dd8\u0dad \u0db4\u0dd9\u0daf\u0dd9\u0dc3 \u00a0\u0d85\u0d9a\u0dca\u0dc2\u0dba \u0dc0\u0da7\u0dcf \u0db7\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba \u0d9a\u0dbd\u0dc0\u0dd2\u0da7 \u0da2\u0db1\u0db1\u0dba \u0dc0\u0db1 \u0d9d\u0db1 \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 V<sub>0<\/sub> ,<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\boxed{V\\;=\\pi\\int\\;y^{2\\;}dx}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u0d8b\u0daf\u0dcf:-<\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\">\r\n<li>\u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0dd9\u0db1\u0dd4\u0dad\u0dca \u00a0<em>x=1,x=2,y=0 <\/em>\u00a0\u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dbd\u0dd2\u0db1\u0dd4\u0dad\u0dca \u0d86\u0dc0\u0dd8\u0dad \u0db4\u0dd9\u0daf\u0dd9\u0dc3 \u00a0\u0d85\u0d9a\u0dca\u0dc2\u0dba \u0dc0\u0da7\u0dcf 2\u03c0 \u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0dd2\u0db1\u0dca \u0db7\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba \u0d9a\u0dbd\u0dc0\u0dd2\u0da7 \u0da2\u0db1\u0db1\u0dba \u0dc0\u0db1 \u0d9d\u0db1 \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">V_o=\\;\\pi\\int_1^2(\\sqrt{x^2+1})^2\\;\\operatorname dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">V_o=\\;\\pi\\int_1^2(x^2+1)\\;\\operatorname dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">V_o=\\;\\pi{\\left[\\frac13x^3+x\\right]^2}_1<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">V_o=\\pi\\left\\{\\left[\\frac13.2^3+2\\right]\\;-\\;\\left[\\frac13+1\\right]\\right\\}<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">V_o=\\frac{10\\pi}3\\text{\u00a0\u0db4\u0dbb\u0dd2\u0db8\u0dcf \u0d92\u0d9a\u0d9a}<\/span><\/p>\r\n\r\n\r\n\r\n<p>2. <span class=\"wp-katex-eq\" data-display=\"false\">0\\leq y\\leq e^{x\\;\\;\\;}\\text{\u0dc4\u0dcf}\\;0\\leq x\\leq3\\;<\/span> \u0d85\u0dad\u0dbb \u0dc0\u0dd6 \u0db4\u0dca\u200d\u0dbb\u0daf\u0dda\u0dc1\u0dba x \u0d85\u0d9a\u0dca\u0dc2\u0dba \u0dc0\u0da7\u0dcf 2<span class=\"wp-katex-eq\" data-display=\"false\">\\pi<\/span> \u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0dd2\u0db1\u0dca \u0db7\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca \u0da2\u0db1\u0db1\u0dba \u0dc0\u0db1 \u0d9d\u0db1 \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\r\n\r\n\r\n\r\n<p>\u0db8\u0dd9\u0dba\u0dd2\u0db1\u0dca \u0d85\u0daf\u0dc4\u0dc3\u0dca \u0dc0\u0db1\u0dca\u0db1\u0dda \u0daf \u0db4\u0dd9\u0dbb \u0db4\u0dbb\u0dd2\u0daf\u0dd2\u0db8 <em>y=e<sup>x<\/sup><\/em> \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0dd9\u0db1\u0dd4\u0dad\u0dca \u00a0<em>x=0,x=3,y=0 \u00a0<\/em>\u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dbd\u0dd2\u0db1\u0dd4\u0dad\u0dca \u0d86\u0dc0\u0dd8\u0dad \u0db4\u0dd9\u0daf\u0dd9\u0dc3 <em>x <\/em>\u0d85\u0d9a\u0dca\u0dc2\u0dba \u0dc0\u0da7\u0dcf \u0db7\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba \u0d9a\u0dbd\u0dc0\u0dd2\u0da7 \u0da2\u0db1\u0db1\u0dba \u0dc0\u0db1 \u0d9d\u0db1 \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0\u0dba\u0dd2. \u0d91\u0db8 \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 V\u00ad<sub>0<\/sub> \u0db1\u0db8\u0dca,<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">V_o=\\pi\\int_0^3(e^x)^2\\;dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">V_o=\\pi\\int_0^3e^{2x}\\;dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">V_o=\\pi{\\left[\\frac12e^{2x}\\right]^3}_0<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">V_o=\\frac\\pi2\\left\\{\\left[e^6\\right]-\\left[e^0\\right]\\right\\}<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">V_o=\\frac\\pi2\\left(e^6-1\\right)\\;\\text{\u0db4\u0dbb\u0dd2\u0db8\u0dcf\u00a0\u0d92\u0d9a\u0d9a}<\/span><\/p>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?id=1Xfd74wulLDsyEulFDtQfKsXzLBEPrVG4&amp;export=download\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/drive\/folders\/1nckWIt5wB-xVw56bK1UE2TWCsXw7jlNl?usp=sharing\" target=\"_blank\" rel=\"noreferrer noopener\">\u0dad\u0dc0\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>\u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dca \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dc0\u0dbd\u0dd2\u0db1\u0dca \u0db8\u0dcf\u0dba\u0dd2\u0db8\u0dca \u0dc0\u0dd6  \u0db4\u0dca\u200d\u0dbb\u0daf\u0dda\u0dc1\u0dc0\u0dbd \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc4\u0dcf \u0db4\u0dbb\u0dd2\u0db7\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba\u0dd9\u0db1\u0dca \u0dbd\u0dd0\u0db6\u0dd9\u0db1 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