Hỏi đáp về Chương 3 Nguyên hàm, Tích phân và Ứng dụng

A. 2                        

B. 4   

C. 3                        

D. 5

A. \( - \dfrac{1}{4}\sin \left( {\pi  - 2a} \right) - \sin 2a + \pi  - 4a\).

B. \(  \dfrac{1}{4}\left( {\sin \left( {\pi  - 2a} \right) - \sin 2a + \pi  - 4a} \right)\).

C. \( - \dfrac{1}{4}\left( {\sin \left( {\pi  - 2a} \right) - \sin 2a + \pi  - 4a} \right)\).

D. 0.

A. 27ln2.             

B. 72ln27

C. 3ln72.                   

D. Một kết quả khác.

A. Nếu V₁ = V₂ thì chắc chắn suy ra \(f(x) = g(x),\forall x \in [a;b]\).

B. S₁>S₂.

C. V₁ > V₂.

D. Cả 3 phương án trên đều sai.

A. \(\dfrac{1}{{20}}{\left( {5x + 3} \right)^4} + C\).  

B. \(\dfrac{1}{{20}}{\left( {5x + 3} \right)^4}\).

C. \(\dfrac{1}{4}{\left( {5x + 3} \right)^4} + C\).           

D. \(\dfrac{1}{5}{\left( {5x + 3} \right)^4} + C\).

A. \(2\ln |x + 1| + \dfrac{{2{x^2} + 2x + 4}}{{x + 1}}\). 

B. \(\ln \left( {x + 1} \right) + \dfrac{{2{x^2} + 2x + 4}}{{x + 1}}\).

C. \(\ln {\left( {x + 1} \right)^2} + \dfrac{{2{x^2} + 3x + 5}}{{x + 1}}\). 

D. \(\dfrac{{2{x^2} + 3x + 5}}{{x + 1}} + \ln {e^2}{\left( {x + 1} \right)^2}\).

A . F’(x) = x.          

B. F’(x) = 1.

C. F’(x) = x – 1.                  

D. F’(x) = \(\dfrac{{{x^2}}}{2} - \dfrac{1}{2}\).

A. \(I = \sin \left( {4x + 2} \right) + C\).        

B. \(I =  - \sin \left( {4x + 3} \right) + C\).

C. \(I = \dfrac{1}{4}\sin \left( {4x + 3} \right) + C\). 

D. \(I = 4\sin \left( {4x + 3} \right) + C\).

A. \(\sqrt 3  - \dfrac{\pi }{3}\)    

B. \(\dfrac{\pi }{3} - 3\)                     

C. \(\dfrac{{{\pi ^2}}}{3} - \pi \sqrt 3 \)  

D. \(\pi \sqrt 3  - \dfrac{{{\pi ^2}}}{3}\).

A. \(I = \ln |x - 3| - \dfrac{{16}}{{x - 3}} + C\).    

B. \(I = \dfrac{1}{5}\ln |x - 3| - \dfrac{{16}}{{x - 3}} + C\).

C. \(I = \ln |x - 3| + \dfrac{{16}}{{x - 3}} + C\).     

D. \(I = 5\ln |x - 3| - \dfrac{{16}}{{x - 3}} + C\).

A. \(\int {\dfrac{{dx}}{{6x - 2}} = 6\ln |6x - 2| + C} \).

B. \(\int {\dfrac{{dx}}{{6x - 2}} = \dfrac{1}{6}\ln |6x - 2| + C} \).

C. \(\int {\dfrac{{dx}}{{6x - 2}} = \dfrac{1}{2}\ln |6x - 2| + C} \).

D. \(\int {\dfrac{{dx}}{{6x - 2}} = \ln |6x - 2| + C} \).

A. – 2   

B. \(\dfrac{{13}}{6}\)   

C. \(\ln 2 - \dfrac{3}{4}\)

D. \(\ln 3 - \dfrac{3}{5}\).

A. \(I = 2\int\limits_0^1 {dt} \).     

B. \(I = 2\int\limits_0^{\dfrac{\pi }{4}} {dt} \).

C. \(I = \int\limits_0^{\dfrac{\pi }{3}} {dt} \).          

D. \(I = 2\int\limits_0^{\dfrac{\pi }{6}} {dt} \).

A. \(\pi \int\limits_0^\pi  {{{\sin }^2}x} \,dx\).  

B. \(\dfrac{\pi }{2}\int\limits_0^\pi  {{{\sin }^2}x} \,dx\).

C. \(\dfrac{\pi }{2}\int\limits_0^\pi  {{{\sin }^4}x} \,dx\).   

D. \(\pi \int\limits_0^\pi  {\sin x} \,dx\).

A. \(\ln \dfrac{3}{2}\)      

B. \(\dfrac{1}{2}\)                           

C. ln 2       

D. ln2 + 1 

A. \(I = 2\int\limits_8^9 {\sqrt u du} \). 

B. \(I = \dfrac{1}{2}\int\limits_8^9 {\sqrt u \,du} \).

C. \(I = \int\limits_8^9 {\sqrt u \,du} \).               

D. \(I = \int\limits_9^8 {\sqrt u \,du} \)

A. \(2\ln 2 + 3\).   

B. \(\dfrac{{\ln 2}}{2} + \dfrac{3}{4}\).

C. \(\ln 2 + \dfrac{3}{2}\).   

D. \(\ln 2 + 1\). 

A. \(4\cos x + \ln x + C\).     

B. \(4\cos x + \dfrac{1}{x} + C\).

C. \(4\sin x - \dfrac{1}{x} + C\).         

D. \(4\sin x + \dfrac{1}{x} + C\).

A. \(I = \dfrac{1}{2}\).    

B. \(I = \dfrac{{3{e^2} + 1}}{4}\).

C. \(I = \dfrac{{{e^2} + 1}}{4}\).    

D. \(I = \dfrac{{{e^2} - 1}}{4}\).

A. \(\left\{ \begin{array}{l}A =  - 2\\B =  - \dfrac{2}{\pi }\end{array} \right.\).  

B. \(\left\{ \begin{array}{l}A = 2\\B =  - \dfrac{2}{\pi }\end{array} \right.\).

C. \(\left\{ \begin{array}{l}A =  - 2\\B = \dfrac{2}{\pi }\end{array} \right.\).   

D. \(\left\{ \begin{array}{l}B = 2\\A =  - \dfrac{2}{\pi }\end{array} \right.\)

A. \(I = \int\limits_{\dfrac{1}{2}}^1 {\dfrac{{2t}}{{1 + 1}}\,dt} \).  

B. \(I = \int\limits_{\dfrac{0}{2}}^{\dfrac{x}{4}} {\dfrac{{2t}}{{1 + 1}}\,dt} \).

C. \(I =  - \int\limits_{\dfrac{1}{2}}^1 {\dfrac{{2t}}{{1 + 1}}\,dt} \).    

D. \(I =  - \int\limits_{\dfrac{0}{2}}^{\dfrac{x}{4}} {\dfrac{{2t}}{{1 + 1}}\,dt} \).

A. \(\int\limits_a^b {f(x)\,dx = \int\limits_b^a {f(x)\,dx} } \).

B. \(\int\limits_a^b {k.dx = k\left( {b - a} \right),\,\forall k \in R} \).

C. \(\int\limits_a^b {f(x)\,dx =  - \int\limits_b^a {f(x)\,dx} } \)

D. \(\int\limits_a^b {f(x)\,dx = \int\limits_a^c {f(x)\,dx + \int\limits_c^b {f(x)\,dx\,,\,\,\,c \in [a;b]} } } \)

A. 24                              

B. – 7  

C. – 4                             

D. 8 

A. \(\int\limits_a^b {\left| {f(a)} \right|\,dx} \).   

B. \( - \int\limits_a^b {f(x)\,dx} \).

C. \(\int\limits_b^a {f(x)\,dx} \).            

D. \(\int\limits_a^b {f(x)\,dx} \).

A. 6                           

B 46  

C. 26                           

D. 12