Sách Toán – Học Toán – Đề Thi Toán https://booktoan.com Học toán, Đề thi toán, Sách giáo khoa Toán, trắc nghiệm Toán online Mon, 04 May 2026 09:52:29 +0000 vi hourly 1 https://wordpress.org/?v=7.1.3 Ứng Dụng Tích Phân Tính Thể Tích Vật Thể – Các Dạng Bài THPT Quốc Gia https://booktoan.com/ung-dung-tich-phan-tinh-the-tich-vat-the-cac-dang-bai-thpt-quoc-gia.html https://booktoan.com/ung-dung-tich-phan-tinh-the-tich-vat-the-cac-dang-bai-thpt-quoc-gia.html#respond Mon, 04 May 2026 09:52:29 +0000 https://booktoan.com/ung-dung-tich-phan-tinh-the-tich-vat-the-cac-dang-bai-thpt-quoc-gia.html https://booktoan.com/ung-dung-tich-phan-tinh-the-tich-vat-the-cac-dang-bai-thpt-quoc-gia.html/feed 0 CHUYÊN ĐỀ TOÁN 12 – TÍCH PHÂN https://booktoan.com/chuyen-de-toan-12-tich-phan.html https://booktoan.com/chuyen-de-toan-12-tich-phan.html#respond Sat, 12 Aug 2023 08:14:52 +0000 https://booktoan.com/chuyen-de-toan-12-tich-phan.html https://booktoan.com/chuyen-de-toan-12-tich-phan.html/feed 0 Cho hàm số \(f\left( x \right) = \left\{ \begin{array}{l}3{x^2} – 2{\rm{ khi }}x \le 1\\2x – 1{\rm{ khi }}x > 1\end{array} \right.\). Tính \(I = \int\limits_{ – \frac{\pi }{2}}^{\frac{\pi }{2}} {f\left( {1 – \sin x} \right)\cos x{\rm{d}}x} \). https://booktoan.com/cho-ham-so-fleft-x-right-left-beginarrayl3x2-2rm-khi-x-le-12x-1rm-khi-x-1endarray-right-tinh-i-intlimits_-fracpi-2.html https://booktoan.com/cho-ham-so-fleft-x-right-left-beginarrayl3x2-2rm-khi-x-le-12x-1rm-khi-x-1endarray-right-tinh-i-intlimits_-fracpi-2.html#respond Fri, 19 May 2023 17:00:00 +0000 https://booktoan.com/cho-ham-so-fleft-x-right-left-beginarrayl3x2-2rm-khi-x-le-12x-1rm-khi-x-1endarray-right-tinh-i-intlimits_-fracpi-2.html https://booktoan.com/cho-ham-so-fleft-x-right-left-beginarrayl3x2-2rm-khi-x-le-12x-1rm-khi-x-1endarray-right-tinh-i-intlimits_-fracpi-2.html/feed 0 Biết \(I = \int\limits_1^3 {\frac{{3 + \ln x}}{{{{\left( {x + 1} \right)}^2}}}\,} {\rm{d}}x\)\( = a\left( {1 + \ln 3} \right) – b\ln 2\), \(\left( {a\,,\,b \in \mathbb{Q}} \right)\). Giá trị của biểu thức \(T = {a^2} + {b^2}\) là: https://booktoan.com/biet-i-intlimits_13-frac3-ln-xleft-x-1-right2-rmdx-aleft-1-ln-3-right-bln-2-left-ab-in-mathbbq-righ.html https://booktoan.com/biet-i-intlimits_13-frac3-ln-xleft-x-1-right2-rmdx-aleft-1-ln-3-right-bln-2-left-ab-in-mathbbq-righ.html#respond Fri, 19 May 2023 17:00:00 +0000 https://booktoan.com/biet-i-intlimits_13-frac3-ln-xleft-x-1-right2-rmdx-aleft-1-ln-3-right-bln-2-left-ab-in-mathbbq-righ.html https://booktoan.com/biet-i-intlimits_13-frac3-ln-xleft-x-1-right2-rmdx-aleft-1-ln-3-right-bln-2-left-ab-in-mathbbq-righ.html/feed 0 Giả sử tích phân \(I = \int\limits_{ – \frac{\pi }{2}}^{\frac{\pi }{2}} {\frac{{{x^2} + \cos x}}{{1 + {3^x}}}dx} = a{\pi ^3} + b\pi + c\), trong đó \(a,b,c \in \mathbb{Q}\). Tính \(S = 8a + 4b + c\) https://booktoan.com/gia-su-tich-phan-i-intlimits_-fracpi-2fracpi-2-fracx2-cos-x1-3xdx-api-3-bpi-c-trong-do-abc-in-mathbbq-tinh-s.html https://booktoan.com/gia-su-tich-phan-i-intlimits_-fracpi-2fracpi-2-fracx2-cos-x1-3xdx-api-3-bpi-c-trong-do-abc-in-mathbbq-tinh-s.html#respond Fri, 19 May 2023 17:00:00 +0000 https://booktoan.com/gia-su-tich-phan-i-intlimits_-fracpi-2fracpi-2-fracx2-cos-x1-3xdx-api-3-bpi-c-trong-do-abc-in-mathbbq-tinh-s.html https://booktoan.com/gia-su-tich-phan-i-intlimits_-fracpi-2fracpi-2-fracx2-cos-x1-3xdx-api-3-bpi-c-trong-do-abc-in-mathbbq-tinh-s.html/feed 0 Cho hàm số \(y = f\left( x \right)\) liên tục trên khoảng \(\left( {0; + \infty } \right)\) và thỏa mãn \(f\left( {{x^2} + 1} \right) + \frac{{f\left( {\sqrt x } \right)}}{{4x\sqrt x }} = \frac{{2x + 1}}{{2x}}\ln \left( {x + 1} \right)\). Biết \(\int\limits_1^{17} {f\left( x \right){\rm{d}}x = a\ln 5 – 2\ln b + c} \) với \(a,{\rm{ }}b,{\rm{ }}c \in \mathbb{R}\). Tính \(T = a – 3b + 2c\). https://booktoan.com/cho-ham-so-y-fleft-x-right-lien-tuc-tren-khoang-left-0-infty-right-va-thoa-man-fleft-x2-1-right-fracfleft-sqrt-x-right4xsqrt-x.html https://booktoan.com/cho-ham-so-y-fleft-x-right-lien-tuc-tren-khoang-left-0-infty-right-va-thoa-man-fleft-x2-1-right-fracfleft-sqrt-x-right4xsqrt-x.html#respond Fri, 19 May 2023 17:00:00 +0000 https://booktoan.com/cho-ham-so-y-fleft-x-right-lien-tuc-tren-khoang-left-0-infty-right-va-thoa-man-fleft-x2-1-right-fracfleft-sqrt-x-right4xsqrt-x.html https://booktoan.com/cho-ham-so-y-fleft-x-right-lien-tuc-tren-khoang-left-0-infty-right-va-thoa-man-fleft-x2-1-right-fracfleft-sqrt-x-right4xsqrt-x.html/feed 0 Bên trong hình vuông cạnh \(a\), dựng hình sao bốn cánh đều như hình vẽ sau (các kích thước cần thiết cho như ở trong hình). https://booktoan.com/ben-trong-hinh-vuong-canh-a-dung-hinh-sao-bon-canh-deu-nhu-hinh-ve-sau-cac-kich-thuoc-can-thiet-cho-nhu-o-trong-hinh.html https://booktoan.com/ben-trong-hinh-vuong-canh-a-dung-hinh-sao-bon-canh-deu-nhu-hinh-ve-sau-cac-kich-thuoc-can-thiet-cho-nhu-o-trong-hinh.html#respond Fri, 19 May 2023 17:00:00 +0000 https://booktoan.com/ben-trong-hinh-vuong-canh-a-dung-hinh-sao-bon-canh-deu-nhu-hinh-ve-sau-cac-kich-thuoc-can-thiet-cho-nhu-o-trong-hinh.html https://booktoan.com/ben-trong-hinh-vuong-canh-a-dung-hinh-sao-bon-canh-deu-nhu-hinh-ve-sau-cac-kich-thuoc-can-thiet-cho-nhu-o-trong-hinh.html/feed 0 Cho \(F\left( x \right) = \frac{1}{{2{x^2}}}\) là một nguyên hàm của hàm số \(\frac{{f\left( x \right)}}{x}\). Gọi \(G\left( x \right)\) là một nguyên hàm của hàm số \(f’\left( x \right)\ln x\) và \(G\left( 1 \right) = – \frac{1}{2}\). Phương trình \(G\left( {2{x^2} – 1} \right) = m\) có 4 nghiệm phân biệt khi \(m\) thuộc khoảng nào? https://booktoan.com/cho-fleft-x-right-frac12x2-la-mot-nguyen-ham-cua-ham-so-fracfleft-x-rightx-goi-gleft-x-right-la-mot-nguyen-ham-cua-ham-so-fleft-x-rig.html https://booktoan.com/cho-fleft-x-right-frac12x2-la-mot-nguyen-ham-cua-ham-so-fracfleft-x-rightx-goi-gleft-x-right-la-mot-nguyen-ham-cua-ham-so-fleft-x-rig.html#respond Fri, 19 May 2023 17:00:00 +0000 https://booktoan.com/cho-fleft-x-right-frac12x2-la-mot-nguyen-ham-cua-ham-so-fracfleft-x-rightx-goi-gleft-x-right-la-mot-nguyen-ham-cua-ham-so-fleft-x-rig.html https://booktoan.com/cho-fleft-x-right-frac12x2-la-mot-nguyen-ham-cua-ham-so-fracfleft-x-rightx-goi-gleft-x-right-la-mot-nguyen-ham-cua-ham-so-fleft-x-rig.html/feed 0 Tính \(\int\limits_1^{\frac{{\sqrt 6 + \sqrt 2 }}{2}} {\frac{{ – 4{x^4} + {x^2} – 3}}{{{x^4} + 1}}{\rm{d}}x} = \frac{{\sqrt 2 }}{8}\left( {a\sqrt 3 + b + c\pi } \right) + 4\), với \(a,b,c\) là các số nguyên. Khi đó \(a + {b^2} + {c^4}\) bằng https://booktoan.com/tinh-intlimits_1fracsqrt-6-sqrt-2-2-frac-4x4-x2-3x4-1rmdx-fracsqrt-2-8left-asqrt-3-b-cpi-right-4-voi-a.html https://booktoan.com/tinh-intlimits_1fracsqrt-6-sqrt-2-2-frac-4x4-x2-3x4-1rmdx-fracsqrt-2-8left-asqrt-3-b-cpi-right-4-voi-a.html#respond Fri, 19 May 2023 17:00:00 +0000 https://booktoan.com/tinh-intlimits_1fracsqrt-6-sqrt-2-2-frac-4x4-x2-3x4-1rmdx-fracsqrt-2-8left-asqrt-3-b-cpi-right-4-voi-a.html https://booktoan.com/tinh-intlimits_1fracsqrt-6-sqrt-2-2-frac-4x4-x2-3x4-1rmdx-fracsqrt-2-8left-asqrt-3-b-cpi-right-4-voi-a.html/feed 0 Cho hàm số bậc nhất \(f\left( x \right)\) có đồ thị như hình vẽ bên dưới. Tích phân \(\int\limits_0^4 {f\left( x \right).dx} \) bằng https://booktoan.com/cho-ham-so-bac-nhat-fleft-x-right-co-do-thi-nhu-hinh-ve-ben-duoi-tich-phan-intlimits_04-fleft-x-right-dx-bang.html https://booktoan.com/cho-ham-so-bac-nhat-fleft-x-right-co-do-thi-nhu-hinh-ve-ben-duoi-tich-phan-intlimits_04-fleft-x-right-dx-bang.html#respond Fri, 19 May 2023 17:00:00 +0000 https://booktoan.com/cho-ham-so-bac-nhat-fleft-x-right-co-do-thi-nhu-hinh-ve-ben-duoi-tich-phan-intlimits_04-fleft-x-right-dx-bang.html https://booktoan.com/cho-ham-so-bac-nhat-fleft-x-right-co-do-thi-nhu-hinh-ve-ben-duoi-tich-phan-intlimits_04-fleft-x-right-dx-bang.html/feed 0