Sách Toán – Học Toán – Đề Thi Toán https://booktoan.com Học toán, Đề thi toán, Sách giáo khoa Toán, trắc nghiệm Toán online Wed, 23 Jun 2021 16:55:09 +0000 vi hourly 1 https://wordpress.org/?v=7.1.2 Cho hàm số \(f(x) = \left\{ {\begin{array}{*{20}{l}}{4x}&{{\rm{ khi }}x > 2}\\{ – 2x + 12}&{{\rm{ khi }}x \le 2}\end{array}} \right.\). Tính tích phân \(I = \int\limits_0^{\sqrt 3 } {\frac{{x.f\left( {\sqrt {{x^2} + 1} } \right)}}{{\sqrt {{x^2} + 1} }}} dx + \int\limits_{\ln 2}^{\ln 3} {{e^{2x}}.f\left( {1 + {e^{2x}}} \right)dx} \) https://booktoan.com/cho-ham-so-fx-left-beginarray20l4xrm-khi-x-2-2x-12rm-khi-x-le-2endarray-right-tinh-tich-phani-intlimits_0.html https://booktoan.com/cho-ham-so-fx-left-beginarray20l4xrm-khi-x-2-2x-12rm-khi-x-le-2endarray-right-tinh-tich-phani-intlimits_0.html#respond Wed, 23 Jun 2021 16:55:09 +0000 https://booktoan.com/?p=177693 https://booktoan.com/cho-ham-so-fx-left-beginarray20l4xrm-khi-x-2-2x-12rm-khi-x-le-2endarray-right-tinh-tich-phani-intlimits_0.html/feed 0 Cho hàm số \(f(x) = \left\{ {\begin{array}{*{20}{l}}{{x^2} – x}&{{\rm{ khi }}x \ge 0}\\x&{{\rm{ khi }}x < 0}\end{array}} \right.\). Khi đó \(I = \int\limits_{ – \frac{\pi }{2}}^{\frac{\pi }{2}} {\cos xf\left( {\sin x} \right)} dx\)bằng https://booktoan.com/cho-ham-so-fx-left-beginarray20lx2-xrm-khi-x-ge-0xrm-khi-x-0endarray-right-khi-do-i-intlimits_-fracpi.html https://booktoan.com/cho-ham-so-fx-left-beginarray20lx2-xrm-khi-x-ge-0xrm-khi-x-0endarray-right-khi-do-i-intlimits_-fracpi.html#respond Wed, 23 Jun 2021 16:51:47 +0000 https://booktoan.com/?p=177670 https://booktoan.com/cho-ham-so-fx-left-beginarray20lx2-xrm-khi-x-ge-0xrm-khi-x-0endarray-right-khi-do-i-intlimits_-fracpi.html/feed 0 Cho hàm số \(f(x) = \left\{ \begin{array}{l}2{x^2} + 1\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{khi }}x \ge 0\\2{x^2} – x + 1\,\,\,\,\,{\rm{khi }}x < 0\end{array} \right.\). Tính tích phân \(\int\limits_0^{\frac{\pi }{3}} {f\left( {3\cos x – 2} \right)} \sin x{\rm{d}}x\). https://booktoan.com/cho-ham-so-fx-left-beginarrayl2x2-1rmkhi-x-ge-02x2-x-1rmkhi-x-0endarray-right-tinh.html https://booktoan.com/cho-ham-so-fx-left-beginarrayl2x2-1rmkhi-x-ge-02x2-x-1rmkhi-x-0endarray-right-tinh.html#respond Wed, 23 Jun 2021 16:26:23 +0000 https://booktoan.com/?p=177673 https://booktoan.com/cho-ham-so-fx-left-beginarrayl2x2-1rmkhi-x-ge-02x2-x-1rmkhi-x-0endarray-right-tinh.html/feed 0 Cho hàm số \(y = f\left( x \right)\) xác định và liên tục trên \(\mathbb{R}\) thoả \(f\left( {{x^5} + 4x + 3} \right) = 2x + 1,\,\forall x \in \mathbb{R}.\)Tích phân \(\int_{ – 2}^8 {f\left( x \right)} dx\) bằng https://booktoan.com/cho-ham-so-y-fleft-x-right-xac-dinh-va-lien-tuc-tren-mathbbr-thoa-fleft-x5-4x-3-right-2x-1forall-x-in-mathbbr-tich-phan-int_-28.html https://booktoan.com/cho-ham-so-y-fleft-x-right-xac-dinh-va-lien-tuc-tren-mathbbr-thoa-fleft-x5-4x-3-right-2x-1forall-x-in-mathbbr-tich-phan-int_-28.html#respond Wed, 23 Jun 2021 15:25:07 +0000 https://booktoan.com/?p=177664 https://booktoan.com/cho-ham-so-y-fleft-x-right-xac-dinh-va-lien-tuc-tren-mathbbr-thoa-fleft-x5-4x-3-right-2x-1forall-x-in-mathbbr-tich-phan-int_-28.html/feed 0 Cho \(F\left( x \right)\) là một nguyên hàm của hàm số \(f\left( x \right) = \left| {1 + x} \right| – \left| {1 – x} \right|\) trên tập \(\mathbb{R}\) và thỏa mãn \(F\left( 1 \right) = 3\). Tính tổng \(F\left( 0 \right) + F\left( 2 \right) + F\left( { – 3} \right)\). https://booktoan.com/cho-fleft-x-right-la-mot-nguyen-ham-cua-ham-so-fleft-x-right-left-1-x-right-left-1-x-right-tren-tap-mathbbr-va-thoa-man-fleft-1-right.html https://booktoan.com/cho-fleft-x-right-la-mot-nguyen-ham-cua-ham-so-fleft-x-right-left-1-x-right-left-1-x-right-tren-tap-mathbbr-va-thoa-man-fleft-1-right.html#respond Wed, 23 Jun 2021 15:11:34 +0000 https://booktoan.com/?p=177661 https://booktoan.com/cho-fleft-x-right-la-mot-nguyen-ham-cua-ham-so-fleft-x-right-left-1-x-right-left-1-x-right-tren-tap-mathbbr-va-thoa-man-fleft-1-right.html/feed 0 Cho hàm số \(f(x) = \left\{ {\begin{array}{*{20}{l}}{\frac{1}{x}}&{{\rm{ }}khi{\rm{ }}x \ge 1}\\{x + 1}&{{\rm{ }}khi{\rm{ }}x < 1}\end{array}} \right.\). Tích phân \(\int\limits_{ – 2}^1 {f(\sqrt[3]{{1 – x}}){\rm{d}}x}  = \frac{m}{n}\) (\(\frac{m}{n}\) là phân số tối giản), khi đó \(m – 2n\) bằng: https://booktoan.com/cho-ham-so-fx-left-beginarray20lfrac1xrm-khirm-x-ge-1x-1rm-khirm-x-1endarray-right-tich-phan-int.html https://booktoan.com/cho-ham-so-fx-left-beginarray20lfrac1xrm-khirm-x-ge-1x-1rm-khirm-x-1endarray-right-tich-phan-int.html#respond Wed, 23 Jun 2021 14:07:34 +0000 https://booktoan.com/?p=177659 https://booktoan.com/cho-ham-so-fx-left-beginarray20lfrac1xrm-khirm-x-ge-1x-1rm-khirm-x-1endarray-right-tich-phan-int.html/feed 0 Cho hai hàm \(f(x)\) và \(g(x)\)có đạo hàm trên \(\left[ {1;2} \right]\) thỏa mãn \(f(1) = g(1) = 0\) và \(\left\{ \begin{array}{l}\frac{x}{{{{(x + 1)}^2}}}g(x) + 2017x = (x + 1)f'(x)\\\frac{{{x^3}}}{{x + 1}}g'(x) + f(x) = 2018{x^2}\end{array} \right.{\rm{, }}\forall x \in \left[ {1;2} \right].\) Tính tích phân\(I = \int\limits_1^2 {\left[ {\frac{x}{{x + 1}}g(x) – \frac{{x + 1}}{x}f(x)} \right]} dx\). https://booktoan.com/cho-hai-ham-fx-va-gxco-dao-ham-tren-left-12-right-thoa-man-f1-g1-0-valeft-beginarraylfracxx-12gx-2017x-x-1fx.html https://booktoan.com/cho-hai-ham-fx-va-gxco-dao-ham-tren-left-12-right-thoa-man-f1-g1-0-valeft-beginarraylfracxx-12gx-2017x-x-1fx.html#respond Wed, 23 Jun 2021 11:54:44 +0000 https://booktoan.com/cho-hai-ham-fx-va-gxco-dao-ham-tren-left-12-right-thoa-man-f1-g1-0-valeft-beginarraylfracxx-12gx-2017x-x-1fx.html https://booktoan.com/cho-hai-ham-fx-va-gxco-dao-ham-tren-left-12-right-thoa-man-f1-g1-0-valeft-beginarraylfracxx-12gx-2017x-x-1fx.html/feed 0 Cho hàm số \(f(x) = \left\{ \begin{array}{l}3x + 3\,\,\,{\rm{khi }}x < \frac{1}{2}\\x + 4\,\,\,\,\,{\rm{khi }}x \ge \frac{1}{2}\end{array} \right.\). Tính tích phân \(\int\limits_0^{\frac{\pi }{2}} {f\left( {\sin x} \right)} \cos x{\rm{d}}x\). https://booktoan.com/cho-ham-so-fx-left-beginarrayl3x-3rmkhi-x-frac12x-4rmkhi-x-ge-frac12endarray-right-tinh-tich-phan-int.html https://booktoan.com/cho-ham-so-fx-left-beginarrayl3x-3rmkhi-x-frac12x-4rmkhi-x-ge-frac12endarray-right-tinh-tich-phan-int.html#respond Wed, 23 Jun 2021 11:51:43 +0000 https://booktoan.com/cho-ham-so-fx-left-beginarrayl3x-3rmkhi-x-frac12x-4rmkhi-x-ge-frac12endarray-right-tinh-tich-phan-int.html https://booktoan.com/cho-ham-so-fx-left-beginarrayl3x-3rmkhi-x-frac12x-4rmkhi-x-ge-frac12endarray-right-tinh-tich-phan-int.html/feed 0 Cho hàm số \(f(x) = \left\{ \begin{array}{l}1 – {x^2}\,\,\,{\rm{khi }}x \le 1\\2x – 2\,\,\,\,\,{\rm{khi }}x > 1\end{array} \right.\). Tính tích phân \(\int\limits_{ – \frac{\pi }{2}}^{\frac{\pi }{4}} {f\left( {5\sin 2x – 1} \right)} \cos 2x{\rm{d}}x\). https://booktoan.com/cho-ham-so-fx-left-beginarrayl1-x2rmkhi-x-le-12x-2rmkhi-x-1endarray-right-tinh-tich-phan-intlimits_-frac.html https://booktoan.com/cho-ham-so-fx-left-beginarrayl1-x2rmkhi-x-le-12x-2rmkhi-x-1endarray-right-tinh-tich-phan-intlimits_-frac.html#respond Wed, 23 Jun 2021 11:14:32 +0000 https://booktoan.com/cho-ham-so-fx-left-beginarrayl1-x2rmkhi-x-le-12x-2rmkhi-x-1endarray-right-tinh-tich-phan-intlimits_-frac.html https://booktoan.com/cho-ham-so-fx-left-beginarrayl1-x2rmkhi-x-le-12x-2rmkhi-x-1endarray-right-tinh-tich-phan-intlimits_-frac.html/feed 0 Cho hàm số \(f(x) = \left\{ \begin{array}{l}2{x^2} – 1\,\,\,\,\,\,{\rm{khi}}\,\,x < 0\\x – 1\,\,\,\,\,\,\,\,\,\,\,{\rm{khi}}\,\,0 \le x \le 2\\5 – 2x\,\,\,\,\,\,\,\,{\rm{khi}}\,\,x > 2\,\end{array} \right.\). Tính tích phân \(\int\limits_{ – \frac{\pi }{4}}^{\frac{\pi }{4}} {f\left( {2 – 7\tan x} \right)} \frac{1}{{{{\cos }^2}x}}{\rm{d}}x\). https://booktoan.com/cho-ham-so-fx-left-beginarrayl2x2-1rmkhix-0x-1rmkhi0-le-x-le-25-2x.html https://booktoan.com/cho-ham-so-fx-left-beginarrayl2x2-1rmkhix-0x-1rmkhi0-le-x-le-25-2x.html#respond Wed, 23 Jun 2021 10:41:41 +0000 https://booktoan.com/cho-ham-so-fx-left-beginarrayl2x2-1rmkhix-0x-1rmkhi0-le-x-le-25-2x.html https://booktoan.com/cho-ham-so-fx-left-beginarrayl2x2-1rmkhix-0x-1rmkhi0-le-x-le-25-2x.html/feed 0