{"id":2294,"date":"2026-04-25T02:39:59","date_gmt":"2026-04-25T02:39:59","guid":{"rendered":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/toan-thuc-te-chuyen-de-ung-dung-tich-phan-tinh-the-tich\/"},"modified":"2026-04-25T02:39:59","modified_gmt":"2026-04-25T02:39:59","slug":"toan-thuc-te-chuyen-de-ung-dung-tich-phan-tinh-the-tich","status":"publish","type":"post","link":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/toan-thuc-te-chuyen-de-ung-dung-tich-phan-tinh-the-tich\/","title":{"rendered":"To\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 \u1ee8ng d\u1ee5ng t\u00edch ph\u00e2n t\u00ednh th\u1ec3 t\u00edch"},"content":{"rendered":"<div class=\"entry-content single-page\">\n<p>Chia s\u1ebb t\u00e0i li\u1ec7u to\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 \u1ee8ng d\u1ee5ng t\u00edch ph\u00e2n t\u00ednh th\u1ec3 t\u00edch g\u1ed3m c\u00e1c d\u1ea1ng nh\u01b0 v\u1eadt th\u1ec3 c\u00f3 d\u1ea1ng elip ho\u1eb7c parabol; h\u00ecnh c\u1ea7u, h\u00ecnh n\u00f3n, h\u00ecnh c\u1ee5t,\u2026<\/p>\n<div class=\"code-block code-block-2\" style=\"margin: 8px auto; text-align: center; display: block; clear: both;\">\n<div> <\/div>\n<\/div>\n<h2 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-d5700f57cc494ffbbbac69f5ea05f9e2\" id=\"h-n\u1ed9i-dung-tai-li\u1ec7u-toan-th\u1ef1c-t\u1ebf-chuyen-d\u1ec1-\u1ee9ng-d\u1ee5ng-tich-phan-tinh-th\u1ec3-tich\"><span class=\"ez-toc-section\" id=\"Noi_dung_tai_lieu_Toan_thuc_te_chuyen_de_Ung_dung_tich_phan_tinh_the_tich\"><\/span>N\u1ed9i dung t\u00e0i li\u1ec7u To\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 \u1ee8ng d\u1ee5ng t\u00edch ph\u00e2n t\u00ednh th\u1ec3 t\u00edch<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>C\u00e1c d\u1ea1ng v\u1eadt th\u1ec3 v\u00e0 t\u00ecnh hu\u1ed1ng th\u1ef1c t\u1ebf c\u1ee5 th\u1ec3 \u0111\u01b0\u1ee3c \u0111\u1ec1 c\u1eadp bao g\u1ed3m:<\/p>\n<p><strong>V\u1eadt th\u1ec3 c\u00f3 d\u1ea1ng Elip ho\u1eb7c Parabol quay:<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li>C\u00e1i tr\u1ed1ng tr\u01b0\u1eddng (C\u00e2u 1, C\u00e2u 2).<\/li>\n<li>Th\u00f9ng r\u01b0\u1ee3u, th\u00f9ng ch\u1ee9a (C\u00e2u 3, C\u00e2u 7).<\/li>\n<li>L\u1ec1u tr\u1ea1i h\u00ecnh Parabol (C\u00e2u 10).<\/li>\n<li>\u0110\u1ed3ng h\u1ed3 c\u00e1t c\u00f3 thi\u1ebft di\u1ec7n l\u00e0 Parabol (C\u00e2u 19).<\/li>\n<li>S\u00e2n v\u1eadn \u0111\u1ed9ng h\u00ecnh Elip (C\u00e2u 20).<\/li>\n<li>T\u00ednh th\u1ec3 t\u00edch ph\u1ea7n gi\u1edbi h\u1ea1n b\u1edfi Elip v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n quay (C\u00e2u 9).<\/li>\n<\/ul>\n<p><strong>V\u1eadt th\u1ec3 c\u00f3 d\u1ea1ng H\u00ecnh c\u1ea7u, H\u00ecnh n\u00f3n c\u1ee5t ho\u1eb7c s\u1ef1 giao thoa c\u1ee7a c\u00e1c kh\u1ed1i c\u1ea7u:<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li>B\u00ecnh c\u1eafm hoa t\u1ea1o b\u1edfi \u0111\u01b0\u1eddng cong $y=\\sqrt{x-1}$ (C\u00e2u 4).<\/li>\n<li>Lu \u0111\u1ef1ng n\u01b0\u1edbc (c\u1eaft b\u1ecf hai ph\u1ea7n c\u1ee7a kh\u1ed1i c\u1ea7u) (C\u00e2u 6).<\/li>\n<li>Th\u1ec3 t\u00edch ph\u1ea7n chung gi\u1eefa hai kh\u1ed1i c\u1ea7u (C\u00e2u 12).<\/li>\n<li>Kh\u1ed1i tr\u00f2n xoay t\u1ea1o b\u1edfi h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n gi\u1eefa Parabol v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n (C\u00e2u 8).<\/li>\n<li>H\u1ed3 l\u00f4 \u0111\u1ef1ng r\u01b0\u1ee3u (gh\u00e9p gi\u1eefa hai h\u00ecnh c\u1ea7u v\u00e0 h\u00ecnh tr\u1ee5) (C\u00e2u 11).<\/li>\n<\/ul>\n<p><strong>V\u1eadt th\u1ec3 t\u1ea1o th\u00e0nh khi quay H\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u01b0\u1eddng g\u1ea5p kh\u00fac\/H\u00ecnh ch\u1eef nh\u1eadt:<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li>Quay h\u00ecnh ch\u1eef nh\u1eadt b\u1ecb c\u1eaft b\u1ecf ph\u1ea7n h\u00ecnh thang (C\u00e2u 13).<\/li>\n<li>V\u1eadt trang tr\u00ed t\u1ea1o b\u1edfi h\u00ecnh ch\u1eef nh\u1eadt v\u00e0 c\u00e1c \u0111\u01b0\u1eddng cong\/cung tr\u00f2n (C\u00e2u 14, C\u00e2u 15, C\u00e2u 16).<\/li>\n<\/ul>\n<p><strong>B\u00e0i to\u00e1n t\u00ednh th\u1ec3 t\u00edch v\u1eadt th\u1ec3 kh\u00f4ng ph\u1ea3i kh\u1ed1i tr\u00f2n xoay (d\u00f9ng c\u00f4ng th\u1ee9c $V = \\int S(x) dx$):<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li>Th\u1ec3 t\u00edch d\u1ea7u c\u00f2n l\u1ea1i trong b\u1ed3n h\u00ecnh tr\u1ee5 n\u1eb1m ngang (C\u00e2u 17).<\/li>\n<li>Th\u1ec3 t\u00edch n\u01b0\u1edbc trong c\u1ed1c h\u00ecnh tr\u1ee5 b\u1ecb nghi\u00eang (C\u00e2u 21).<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><strong>Xem tr\u01b0\u1edbc t\u00e0i li\u1ec7u:<\/strong><\/p>\n<p class=\"has-text-align-center\"><iframe loading=\"lazy\" allow=\"autoplay\" height=\"480\" src=\"https:\/\/drive.google.com\/file\/d\/1T0dpW6o6Uk8QUbfKxlplx5egB27uHD6l\/preview\" width=\"640\"><\/iframe><\/p>\n<h2 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-1308f070499de923f66cb7709a2a6129\" id=\"h-t\u1ea3i-tai-li\u1ec7u-toan-th\u1ef1c-t\u1ebf-chuyen-d\u1ec1-\u1ee9ng-d\u1ee5ng-tich-phan-tinh-th\u1ec3-tich\"><span class=\"ez-toc-section\" id=\"Tai_tai_lieu_Toan_thuc_te_chuyen_de_Ung_dung_tich_phan_tinh_the_tich\"><\/span>T\u1ea3i t\u00e0i li\u1ec7u To\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 \u1ee8ng d\u1ee5ng t\u00edch ph\u00e2n t\u00ednh th\u1ec3 t\u00edch<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 t\u1ea3i t\u00e0i li\u1ec7u \u00f4n t\u1eadp mi\u1ec5n ph\u00ed \u1edf \u0111\u00e2y nh\u00e9<\/p>\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-white-color has-luminous-vivid-orange-background-color has-text-color has-background has-link-color has-text-align-center wp-element-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/1ccBt_MK8Gbus0Dul7okQC1YwPVXAFr7U?usp=sharing\" rel=\"noreferrer noopener nofollow\" target=\"_blank\"><strong>T\u1ea2I T\u00c0I LI\u1ec6U (\u0110\u1ec0 + \u0110\u00c1P \u00c1N)<\/strong><\/a><\/div>\n<\/div>\n<p>Tham kh\u1ea3o:<strong><a href=\"https:\/\/tailieuonthi.org\/toan-thuc-te-chuyen-de-gia-tri-lon-nhat-nho-nhat-ham-so\/\" rel=\"noreferrer noopener\" target=\"_blank\"> <\/a><a href=\"https:\/\/tailieuonthi.org\/toan-thuc-te-chuyen-de-ung-dung-tich-phan-tinh-dien-tich\/\" rel=\"noreferrer noopener\" target=\"_blank\">To\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 \u1ee8ng d\u1ee5ng t\u00edch ph\u00e2n t\u00ednh di\u1ec7n t\u00edch<\/a><\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Chia s\u1ebb t\u00e0i li\u1ec7u to\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 \u1ee8ng d\u1ee5ng t\u00edch ph\u00e2n t\u00ednh th\u1ec3 t\u00edch g\u1ed3m c\u00e1c d\u1ea1ng nh\u01b0 v\u1eadt th\u1ec3 c\u00f3 d\u1ea1ng elip ho\u1eb7c parabol; h\u00ecnh c\u1ea7u, h\u00ecnh n\u00f3n, h\u00ecnh c\u1ee5t,\u2026 N\u1ed9i dung t\u00e0i li\u1ec7u To\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 \u1ee8ng d\u1ee5ng t\u00edch ph\u00e2n t\u00ednh th\u1ec3 t\u00edch C\u00e1c d\u1ea1ng v\u1eadt th\u1ec3 v\u00e0 t\u00ecnh [&#8230;]\n","protected":false},"author":1,"featured_media":2293,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23,26],"tags":[],"class_list":["post-2294","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tai-lieu-toan","category-toan-12"],"_links":{"self":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2294","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/comments?post=2294"}],"version-history":[{"count":0,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2294\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/2293"}],"wp:attachment":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=2294"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=2294"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=2294"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}