{"id":2239,"date":"2026-04-25T02:37:46","date_gmt":"2026-04-25T02:37:46","guid":{"rendered":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/toan-12-chuong-4-nguyen-ham-tich-phan\/"},"modified":"2026-04-25T02:37:46","modified_gmt":"2026-04-25T02:37:46","slug":"toan-12-chuong-4-nguyen-ham-tich-phan","status":"publish","type":"post","link":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/toan-12-chuong-4-nguyen-ham-tich-phan\/","title":{"rendered":"To\u00e1n 12 Ch\u01b0\u01a1ng 4: Nguy\u00ean H\u00e0m T\u00edch Ph\u00e2n"},"content":{"rendered":"<div class=\"entry-content single-page\">\n<p>Chia s\u1ebb t\u00e0i li\u1ec7u To\u00e1n 12 Ch\u01b0\u01a1ng 4: Nguy\u00ean H\u00e0m T\u00edch Ph\u00e2n c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi. B\u1ed9 t\u00e0i li\u1ec7u bao g\u1ed3m b\u00e0i gi\u1ea3ng, b\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n v\u00e0 l\u1eddi gi\u1ea3i chi ti\u1ebft cho c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng \u00f4n t\u1eadp.<\/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-85a5968f0a886c09a298045d8512e2ba\" id=\"h-n\u1ed9i-dung-tai-li\u1ec7u-ch\u01b0\u01a1ng-nguyen-ham-tich-phan\"><span class=\"ez-toc-section\" id=\"Noi_dung_tai_lieu_Chuong_Nguyen_Ham_Tich_Phan\"><\/span>N\u1ed9i dung t\u00e0i li\u1ec7u Ch\u01b0\u01a1ng Nguy\u00ean H\u00e0m T\u00edch Ph\u00e2n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>B\u1ed9 t\u00e0i li\u1ec7u n\u00e0y bao g\u1ed3m\u00a0b\u00e0i gi\u1ea3ng, l\u1eddi gi\u1ea3i v\u00e0 \u0111\u1ec1 ki\u1ec3m tra\u00a0v\u1ec1\u00a0Nguy\u00ean h\u00e0m t\u00edch ph\u00e2n\u00a0trong m\u00f4n To\u00e1n l\u1edbp 12.<\/p>\n<h3 class=\"wp-block-heading\" id=\"h-cac-ch\u1ee7-d\u1ec1-ch\u01b0\u01a1ng-nguyen-ham-tich-phan-12\"><span class=\"ez-toc-section\" id=\"Cac_chu_de_chuong_Nguyen_ham_tich_phan_12\"><\/span><strong>C\u00e1c ch\u1ee7 \u0111\u1ec1 ch\u01b0\u01a1ng Nguy\u00ean h\u00e0m t\u00edch ph\u00e2n 12<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th>Ch\u1ee7 \u0111\u1ec1<\/th>\n<th>T\u00f3m t\u1eaft<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Nguy\u00ean h\u00e0m<\/td>\n<td>\u0110\u1ecbnh ngh\u0129a nguy\u00ean h\u00e0m, c\u00e1c c\u00f4ng th\u1ee9c nguy\u00ean h\u00e0m c\u01a1 b\u1ea3n (l\u0169y th\u1eeba, l\u01b0\u1ee3ng gi\u00e1c, h\u00e0m m\u0169), v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a nguy\u00ean h\u00e0m. Bao g\u1ed3m c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp v\u1ec1 nguy\u00ean h\u00e0m \u0111a th\u1ee9c, ph\u00e2n th\u1ee9c, c\u0103n th\u1ee9c, l\u01b0\u1ee3ng gi\u00e1c v\u00e0 h\u00e0m m\u0169, loga, c\u00f9ng v\u1edbi c\u00e1c b\u00e0i to\u00e1n t\u1ed5ng h\u1ee3p v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf (v\u00ed d\u1ee5: chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a v\u1eadt r\u01a1i).<\/td>\n<\/tr>\n<tr>\n<td>T\u00edch ph\u00e2n<\/td>\n<td>Kh\u00e1i ni\u1ec7m di\u1ec7n t\u00edch h\u00ecnh thang cong, \u0111\u1ecbnh ngh\u0129a t\u00edch ph\u00e2n, \u00fd ngh\u0129a h\u00ecnh h\u1ecdc c\u1ee7a t\u00edch ph\u00e2n, v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a t\u00edch ph\u00e2n. Bao g\u1ed3m c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp s\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t t\u00edch ph\u00e2n v\u00e0 t\u00edch ph\u00e2n l\u0169y th\u1eeba, v\u1edbi nhi\u1ec1u v\u00ed d\u1ee5 minh h\u1ecda chi ti\u1ebft v\u1ec1 gi\u1ea3i b\u00e0i t\u1eadp.<\/td>\n<\/tr>\n<tr>\n<td>\u1ee8ng d\u1ee5ng h\u00ecnh h\u1ecdc c\u1ee7a T\u00edch ph\u00e2n<\/td>\n<td>\u1ee8ng d\u1ee5ng t\u00edch ph\u00e2n \u0111\u1ec3 t\u00ednh di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng (gi\u1edbi h\u1ea1n b\u1edfi m\u1ed9t \u0111\u1ed3 th\u1ecb, tr\u1ee5c ho\u00e0nh, v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng; ho\u1eb7c gi\u1edbi h\u1ea1n b\u1edfi hai \u0111\u1ed3 th\u1ecb v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng) v\u00e0 t\u00ednh th\u1ec3 t\u00edch v\u1eadt th\u1ec3, bao g\u1ed3m th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay. Ph\u1ea7n n\u00e0y c\u0169ng cung c\u1ea5p c\u00e1c ph\u01b0\u01a1ng ph\u00e1p v\u00e0 v\u00ed d\u1ee5 gi\u1ea3i b\u00e0i t\u1eadp c\u1ee5 th\u1ec3.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p class=\"has-text-align-left\"><strong>Xem tr\u01b0\u1edbc t\u00e0i li\u1ec7u:<\/strong><\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" alt=\"To\u00e1n 12 Ch\u01b0\u01a1ng 4: Nguy\u00ean H\u00e0m T\u00edch Ph\u00e2n\" class=\"wp-image-8452\" height=\"674\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/image-17.jpg\" width=\"1179\"\/><\/figure>\n<h3 class=\"wp-block-heading\" id=\"h-cac-d\u1ea1ng-bai-t\u1eadp-ch\u01b0\u01a1ng-nguyen-ham-tich-phan\"><span class=\"ez-toc-section\" id=\"Cac_dang_bai_tap_chuong_Nguyen_ham_tich_phan\"><\/span>C\u00e1c d\u1ea1ng b\u00e0i t\u1eadp ch\u01b0\u01a1ng Nguy\u00ean h\u00e0m t\u00edch ph\u00e2n <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>B\u00e0i 1: Nguy\u00ean h\u00e0m (Antiderivatives)Ph\u1ea7n b\u00e0i t\u1eadp c\u1ee7a chuy\u00ean \u0111\u1ec1 Nguy\u00ean h\u00e0m \u0111\u01b0\u1ee3c chia th\u00e0nh c\u00e1c d\u1ea1ng c\u01a1 b\u1ea3n v\u00e0 n\u00e2ng cao:<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li>D\u1ea1ng 1: Nguy\u00ean h\u00e0m \u0111a th\u1ee9c\u00a0(Polynomial Antiderivatives).<\/li>\n<li>D\u1ea1ng 2: Nguy\u00ean h\u00e0m ph\u00e2n th\u1ee9c\u00a0(Rational Function Antiderivatives) \u2013 t\u1eadp trung v\u00e0o c\u00e1c c\u00f4ng th\u1ee9c <img loading=\"lazy\" decoding=\"async\" alt=\"\\int \\frac{1}{x} dx\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"22\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-7e35604dd396205832d3b4d84c4c438a_l3.png\" style=\"vertical-align: -6px;\" title=\"Rendered by QuickLaTeX.com\" width=\"45\"\/>, <img loading=\"lazy\" decoding=\"async\" alt=\"\\int \\frac{1}{ax+b} dx\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"24\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-cea4320ee5e0d5580d097bb9e8cdc44b_l3.png\" style=\"vertical-align: -8px;\" title=\"Rendered by QuickLaTeX.com\" width=\"69\"\/>, v\u00e0 c\u00e1c d\u1ea1ng ph\u00e2n t\u00edch.<\/li>\n<li>D\u1ea1ng 3: Nguy\u00ean h\u00e0m c\u0103n th\u1ee9c\u00a0(Radical Antiderivatives) \u2013 s\u1eed d\u1ee5ng ph\u00e9p \u0111\u1ed5i bi\u1ebfn \u0111\u1ec3 \u0111\u01b0a v\u1ec1 nguy\u00ean h\u00e0m h\u00e0m l\u0169y th\u1eeba.<\/li>\n<li>D\u1ea1ng 4: Nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c\u00a0(Trigonometric Function Antiderivatives) \u2013 \u00e1p d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n nh\u01b0 <img loading=\"lazy\" decoding=\"async\" alt=\"\\int \\cos x dx\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"20\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-56ccc1a7fbbc2094803009056cd6e7d4_l3.png\" style=\"vertical-align: -6px;\" title=\"Rendered by QuickLaTeX.com\" width=\"70\"\/>, <img loading=\"lazy\" decoding=\"async\" alt=\"\\int \\sin x dx\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"20\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-90ca373e27842712596cd077a507d7c5_l3.png\" style=\"vertical-align: -6px;\" title=\"Rendered by QuickLaTeX.com\" width=\"68\"\/>, v\u00e0 c\u00e1c c\u00f4ng th\u1ee9c m\u1edf r\u1ed9ng.<\/li>\n<li>D\u1ea1ng 5: Nguy\u00ean h\u00e0m h\u00e0m m\u0169, loga\u00a0(Exponential and Logarithmic Function Antiderivatives) \u2013 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c cho <img loading=\"lazy\" decoding=\"async\" alt=\"e^x\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-c335b1938fdaa8fbab5fca4f5295025e_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"16\"\/> v\u00e0 <img loading=\"lazy\" decoding=\"async\" alt=\"a^x\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-09686153d5fb48e970a7692859475db1_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"17\"\/>.<\/li>\n<li>D\u1ea1ng 6: B\u00e0i t\u1eadp t\u1ed5ng h\u1ee3p\u00a0\u2013 c\u00e1c b\u00e0i to\u00e1n k\u1ebft h\u1ee3p nhi\u1ec1u ph\u01b0\u01a1ng ph\u00e1p ho\u1eb7c y\u00eau c\u1ea7u t\u00ecm h\u00e0m s\u1ed1 <img loading=\"lazy\" decoding=\"async\" alt=\"f(x)\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"19\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-153268b89486473ac6434ff7c62add12_l3-1.png\" style=\"vertical-align: -5px;\" title=\"Rendered by QuickLaTeX.com\" width=\"34\"\/> khi bi\u1ebft <img loading=\"lazy\" decoding=\"async\" alt=\"f'(x)\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"19\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-fd8b0e4e3a66c986a3d5e3bc8daa3469_l3-1.png\" style=\"vertical-align: -5px;\" title=\"Rendered by QuickLaTeX.com\" width=\"38\"\/> v\u00e0 \u0111i\u1ec1u ki\u1ec7n ban \u0111\u1ea7u.<\/li>\n<li>D\u1ea1ng 7: To\u00e1n th\u1ef1c t\u1ebf\u00a0\u2013 \u1ee9ng d\u1ee5ng Nguy\u00ean h\u00e0m \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n v\u1eadt l\u00fd, v\u00ed d\u1ee5: t\u00ecm v\u1eadn t\u1ed1c v\u00e0 qu\u00e3ng \u0111\u01b0\u1eddng khi bi\u1ebft gia t\u1ed1c.<\/li>\n<\/ul>\n<p><strong>2. B\u00e0i 2: T\u00edch ph\u00e2n (Integrals)Ph\u1ea7n b\u00e0i t\u1eadp c\u1ee7a chuy\u00ean \u0111\u1ec1 T\u00edch ph\u00e2n t\u1eadp trung v\u00e0o vi\u1ec7c \u00e1p d\u1ee5ng \u0111\u1ecbnh ngh\u0129a v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t:<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li>D\u1ea1ng 1: S\u1eed d\u1ee5ng c\u00e1c t\u00ednh ch\u1ea5t c\u1ee7a t\u00edch ph\u00e2n\u00a0\u2013 \u00e1p d\u1ee5ng c\u00e1c t\u00ednh ch\u1ea5t nh\u01b0 <img loading=\"lazy\" decoding=\"async\" alt=\"\\int_a^b kf(x) dx = k \\int_a^b f(x) dx\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"24\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-abbb8df82eca0b5b4c9115f5258b2b3a_l3.png\" style=\"vertical-align: -6px;\" title=\"Rendered by QuickLaTeX.com\" width=\"197\"\/>, <img loading=\"lazy\" decoding=\"async\" alt=\"\\int_a^b [f(x) \\pm g(x)] dx = \\int_a^b f(x) dx \\pm \\int_a^b g(x) dx\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"24\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-5aab8c5fa16cebbd0a5b2f4f543690c6_l3.png\" style=\"vertical-align: -6px;\" title=\"Rendered by QuickLaTeX.com\" width=\"331\"\/>, v\u00e0 t\u00ednh ch\u1ea5t ch\u00e8n c\u1eadn <img loading=\"lazy\" decoding=\"async\" alt=\"\\int_a^b f(x) dx = \\int_a^c f(x) dx + \\int_c^b f(x) dx\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"24\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-c4b2da1553168dcd53619829d6f23820_l3.png\" style=\"vertical-align: -6px;\" title=\"Rendered by QuickLaTeX.com\" width=\"271\"\/>.<\/li>\n<li>D\u1ea1ng 2: T\u00edch ph\u00e2n l\u0169y th\u1eeba\u00a0\u2013 t\u00ednh c\u00e1c t\u00edch ph\u00e2n c\u1ee7a h\u00e0m s\u1ed1 d\u1ea1ng <img loading=\"lazy\" decoding=\"async\" alt=\"x^n\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-e1332dc68d130351055140072719fd6a_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"18\"\/> v\u00e0 <img loading=\"lazy\" decoding=\"async\" alt=\"(ax+b)^n\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"19\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-e913121116c0a7773df3cff1b813655a_l3.png\" style=\"vertical-align: -5px;\" title=\"Rendered by QuickLaTeX.com\" width=\"70\"\/>.<\/li>\n<\/ul>\n<p><strong>3. B\u00e0i 3: \u1ee8ng d\u1ee5ng h\u00ecnh h\u1ecdc c\u1ee7a T\u00edch ph\u00e2nPh\u1ea7n n\u00e0y t\u1eadp trung v\u00e0o c\u00e1c \u1ee9ng d\u1ee5ng h\u00ecnh h\u1ecdc c\u1ee7a T\u00edch ph\u00e2n:<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li>D\u1ea1ng 1: T\u00ednh di\u1ec7n t\u00edch gi\u1edbi h\u1ea1n b\u1edfi 1 \u0111\u1ed3 th\u1ecb\u00a0\u2013 t\u00ednh di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 <img loading=\"lazy\" decoding=\"async\" alt=\"y=f(x)\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"19\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-563e77d38be1a1676b7b690db618a991_l3-1.png\" style=\"vertical-align: -5px;\" title=\"Rendered by QuickLaTeX.com\" width=\"67\"\/>, tr\u1ee5c ho\u00e0nh, v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng <img loading=\"lazy\" decoding=\"async\" alt=\"x=a\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"8\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-cdfeaf810c29f95c6c4c74129390b8a7_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"43\"\/>, <img loading=\"lazy\" decoding=\"async\" alt=\"x=b\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-9d44a1e7b2ae069f376ecbf07ca32b62_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"42\"\/>.<\/li>\n<li>D\u1ea1ng 2: T\u00ednh di\u1ec7n t\u00edch gi\u1edbi h\u1ea1n b\u1edfi 2 hai \u0111\u1ed3 th\u1ecb\u00a0\u2013 t\u00ednh di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb hai h\u00e0m s\u1ed1 <img loading=\"lazy\" decoding=\"async\" alt=\"y=f_1(x)\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"19\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-24d90d7bb00ef63e3ecd856970042dfd_l3.png\" style=\"vertical-align: -5px;\" title=\"Rendered by QuickLaTeX.com\" width=\"72\"\/>, <img loading=\"lazy\" decoding=\"async\" alt=\"y=f_2(x)\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"19\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-57d2b73296d07a026132b2665287bade_l3.png\" style=\"vertical-align: -5px;\" title=\"Rendered by QuickLaTeX.com\" width=\"72\"\/>, v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng <img loading=\"lazy\" decoding=\"async\" alt=\"x=a\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"8\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-cdfeaf810c29f95c6c4c74129390b8a7_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"43\"\/>, <img loading=\"lazy\" decoding=\"async\" alt=\"x=b\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-9d44a1e7b2ae069f376ecbf07ca32b62_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"42\"\/>.<\/li>\n<\/ul>\n<p>Ngo\u00e0i ra, ph\u1ea7n l\u00fd thuy\u1ebft c\u1ee7a B\u00e0i 3 c\u0169ng \u0111\u1ec1 c\u1eadp \u0111\u1ebfn\u00a0T\u00ednh th\u1ec3 t\u00edch h\u00ecnh kh\u1ed1i, bao g\u1ed3m:<\/p>\n<ul class=\"wp-block-list\">\n<li>T\u00ednh th\u1ec3 t\u00edch v\u1eadt th\u1ec3\u00a0theo c\u00f4ng th\u1ee9c <img loading=\"lazy\" decoding=\"async\" alt=\"V = \\int_a^b S(x) dx\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"24\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-6fff7fb16548bf68eace1d0ff7f40db2_l3.png\" style=\"vertical-align: -6px;\" title=\"Rendered by QuickLaTeX.com\" width=\"114\"\/>.<\/li>\n<li>T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay\u00a0khi quay h\u00ecnh ph\u1eb3ng quanh tr\u1ee5c Ox theo c\u00f4ng th\u1ee9c <img loading=\"lazy\" decoding=\"async\" alt=\"V = \\pi \\int_a^b [f(x)]^2 dx\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"24\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-14a347c6fc95f8761f68f8bdd0a17962_l3.png\" style=\"vertical-align: -6px;\" title=\"Rendered by QuickLaTeX.com\" width=\"141\"\/>.<\/li>\n<\/ul>\n<h2 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-4ffdc6df6c55e8c152f8087c71c062e6\" id=\"h-t\u1ea3i-tai-li\u1ec7u-toan-12-ch\u01b0\u01a1ng-4-nguyen-ham-tich-phan\"><span class=\"ez-toc-section\" id=\"Tai_tai_lieu_Toan_12_Chuong_4_Nguyen_Ham_Tich_Phan\"><\/span>T\u1ea3i t\u00e0i li\u1ec7u To\u00e1n 12 Ch\u01b0\u01a1ng 4: Nguy\u00ean H\u00e0m T\u00edch Ph\u00e2n<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\/1N_y8QBCCaYp5MsQ0rIhjl7zqupbyf5uM?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-12-cac-so-dac-trung-do-muc-do-phan-tan\/\" rel=\"noreferrer noopener\" target=\"_blank\">To\u00e1n 12 C\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n cho m\u1eabu s\u1ed1 gh\u00e9p nh\u00f3m<\/a><\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Chia s\u1ebb t\u00e0i li\u1ec7u To\u00e1n 12 Ch\u01b0\u01a1ng 4: Nguy\u00ean H\u00e0m T\u00edch Ph\u00e2n c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi. B\u1ed9 t\u00e0i li\u1ec7u bao g\u1ed3m b\u00e0i gi\u1ea3ng, b\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n v\u00e0 l\u1eddi gi\u1ea3i chi ti\u1ebft cho c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng \u00f4n t\u1eadp. N\u1ed9i dung t\u00e0i li\u1ec7u Ch\u01b0\u01a1ng Nguy\u00ean H\u00e0m T\u00edch Ph\u00e2n B\u1ed9 [&#8230;]\n","protected":false},"author":1,"featured_media":2220,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22,23,26],"tags":[],"class_list":["post-2239","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tai-lieu-thpt","category-tai-lieu-toan","category-toan-12"],"_links":{"self":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2239","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=2239"}],"version-history":[{"count":0,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2239\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/2220"}],"wp:attachment":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=2239"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=2239"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=2239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}