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

A. \({e^3} - \dfrac{7}{2}{e^2} + \ln \left( {1 + e} \right)\).  

B. \({e^2} - 7e + \dfrac{1}{{e + 1}}\).

C. \({e^3} - \dfrac{7}{2}{e^2} - \dfrac{1}{{{{\left( {e + 1} \right)}^2}}}\). 

D. \({e^3} - 7{e^2} - \ln \left( {1 + e} \right)\).

A. \(\dfrac{1}{{x{{\ln }^3}x}}\).                  

B. \(x{\ln ^3}x\).

C. \(\dfrac{{{x^2}}}{{{{\ln }^3}x}}\).                      

D. \(\dfrac{{{{\ln }^3}x}}{x}\).

A. \(\dfrac{6}{7}\)    

B. \(\dfrac{7}{6}\)  

C. 1      

D. 2   

A. \({\left( {a - x} \right)^{\dfrac{5}{2}}} + ax + C\). 

B. \( - \dfrac{2}{5}{\left( {a - x} \right)^{\dfrac{5}{2}}} + ax + C\).

C.\({\left( {a - x} \right)^{\dfrac{5}{2}}} - a + C\).      

D. \(\dfrac{2}{5}{\left( {a - x} \right)^{\dfrac{5}{2}}} - \dfrac{2}{3}a{\left( {a - x} \right)^{\dfrac{3}{2}}} + C\).

A. \({V_y} = 12\pi \).         

B. \({V_y} = 8\pi \). 

C. \({V_y} = 18\pi \).     

D. \({V_y} = 16\pi \). 

A. \( - \dfrac{1}{x} - \dfrac{2}{{{x^2}}} - \dfrac{4}{{3{x^2}}} + C\).

B. \(\dfrac{1}{x} - \dfrac{2}{{{x^2}}} - \dfrac{4}{{3{x^2}}} + C\).

C. \( - \dfrac{1}{x} - \dfrac{1}{{{x^2}}} - \dfrac{1}{{{x^3}}} + C\).    

D. \( - \dfrac{1}{x} + \dfrac{2}{{{x^2}}} - \dfrac{4}{{3{x^2}}} + C\).

A. 32                              

B. 34   

C. 46                              

D. 40 

A. \( - \dfrac{1}{4}\cos 2x + C\)    

B. \(\dfrac{1}{2}{\sin ^2}x + C\).

C. \( - \dfrac{1}{2}{\cos ^2}x + C\).              

D. \(\dfrac{1}{2}\cos 2x + C\).

A. \( - \dfrac{{{\pi ^2}}}{4}\)        

B. \(\pi^2\) 

C. \(\dfrac{{{\pi ^2}}}{2}\)          

D. \( - \dfrac{{{\pi ^2}}}{2}\) 

A. \({x^2}.\sin x + x.\cos x - 2\sin x + C\).  

B. \({x^2}.\sin x + 2x.\cos x - 2\sin x + C\).

C. \(x.\sin x + 2x.\cos x + C\).      

D. \(2x.\cos x + \sin  + C\).

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

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

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

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

A. \( - \dfrac{3}{4}\)                       

B. \(\dfrac{3}{4}\) 

C.  \( - \dfrac{4}{3}\)        

D. \(\dfrac{4}{3}\)  

A. \(\int\limits_a^b {f(3x + 5)\,dx = F(3x + 5)\left| \begin{array}{l}b\\a\end{array} \right.} \).

B. \(\int\limits_a^b {f(x + 1)\,dx = F(x)\left| \begin{array}{l}b\\a\end{array} \right.} \).

C. \(\int\limits_a^b {f(2x)\,dx = 2\left( {F(b) - F(a)} \right)} \). 

D. \(\int\limits_a^b f (x)\,dx = F(b) - F(a)\).

A. \(\dfrac{{2 - e}}{e}\).        

B. e   

C. \(\dfrac{{e - 2}}{e}\)        

D. 2e.

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

B. \(\dfrac{1}{{15}}{\left( {3\ln x + 2} \right)^5} + C\).

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

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

A. y = sin + 1.           

B. y = cosx.

C. y = cotx.                 

D. y = - cosx.

A. \(\dfrac{3}{2}\)         

B. \(\dfrac{{ - 3}}{2}\)

C. \(\dfrac{1}{6}\)     

D. \( - \dfrac{1}{6}\) 

A. \(I = \dfrac{2}{3}{x^3} + \dfrac{1}{3}{x^{ - \dfrac{2}{3}}} - \tan x + C\).

B. \(I = \dfrac{2}{3}{x^3} - \dfrac{3}{2}{x^{\dfrac{2}{3}}} - \tan x + C\).

C. \(I = \dfrac{2}{3}{x^3} - \dfrac{2}{3}\sqrt[3]{{{x^2}}} - \tan x + C\). 

D. \(I = \dfrac{2}{3}{x^3} - \dfrac{3}{2}{x^{\dfrac{2}{3}}} + \tan x + C\).

A. \(\dfrac{{{e^2} - 1}}{2}\).        

B. \(\dfrac{{{e^2} + 1}}{2}\). 

C. \(\dfrac{{{e^2} - 3}}{4}\).    

D. \(\dfrac{{{e^2} - 3}}{2}\). 

A. \(2\ln \dfrac{1}{3}\).                        

B . \(2\ln 3\).

C. \(\dfrac{1}{2}\ln 3\).                        

D. \(\dfrac{1}{2}\ln \dfrac{1}{3}\).

A. 0       

B. -1

C. 1      

D. 2.

A. \(\int {\left[ {f(x).g(x)} \right]} \,dx = \int {f(x)\,dx.\int {g(x)\,dx} } \)

B. \(\int {k.f(x)\,dx = k\int {f(x)\,dx} } \)

C. \(\int {f'(x)\,dx}  = f(x) + C\)

D. \(\int {\left[ {f(x) \pm g(x)} \right]\,dx = \int {f(x)\,dx \pm \int {g(x)\,dx} } } \)

A. I= 27                     

B. I= 3

C. I= 9                        

D. I= 1.

A. \(F(x) = {e^x} - 3{e^{ - 3x}} + C\).

B. \(F(x) = {e^x} + 3{e^{ - x}} + C\).

C. \(F(x) = {e^x} - 3{e^{ - x}} + C\).    

D. \(F(x) = {e^x} + C\).

A. \(I = \int\limits_0^3 {\sqrt u \,du} \).     

B. \(I = \dfrac{2}{3}\sqrt {27} \).

C. \(\int\limits_1^2 {\sqrt u \,du} \).                 

D. \(I = \dfrac{2}{3}{u^{\dfrac{3}{2}}}\left| \begin{array}{l}3\\0\end{array} \right.\).