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

A. \(\left| {\int\limits_{ - 1}^4 {f(x)\,dx} } \right|\).         

B. \(\int\limits_{ - 1}^4 {f(x)\,dx} \).

C. \(\int\limits_{ - 1}^0 {f(x)\,dx + \int\limits_0^4 {f(x)\,dx} } \).

D. \(\int\limits_{ - 1}^0 {f(x)\,dx - \int\limits_0^4 {f(x)\,dx} } \).

A. \( - \cot x - 2\tan x + C\).   

B. \(\cot x - 2\tan x + C\).

C. \(\cot x + 2\tan x + C\).                

D. \( - \cot x + 2\tan x + C\).

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

B. \(\left| {\int\limits_a^b {f(x)\,dx} } \right| \le \int\limits_a^b {|f(x)|\,dx} \).

C. \(\left| {\int\limits_a^b {f(x)\,dx} } \right| = \int\limits_a^b {|f(x)|\,dx} \).   

D. Cả 3 phương án trên đều sai.

A. 29      

B. 5

C. 19   

D. 40 

A. \(\dfrac{4}{3}\)      

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

C. \(\dfrac{5}{3}\)         

D. \(\dfrac{{23}}{{15}}\) 

A. \(\tan x + C\).         

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

C. \(\cot x + C\).           

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

A. \(V = \pi \int\limits_0^2 {\left( {2 - x} \right)\,dx + \pi \int\limits_0^2 {{x^2}\,dx} } \).  

B. \(V = \pi \int\limits_0^2 {\left( {2 - x} \right)\,dx} \).

C. \(V = \pi \int\limits_0^1 {x\,dx + \pi \int\limits_1^2 {\sqrt {2 - x} \,dx} } \).     

D. \(V = \pi \int\limits_0^1 {{x^2}\,dx + \pi \int\limits_1^2 {\left( {2 - x} \right)\,dx} } \).

A. \(F(x) = {e^x} + {x^2} + \dfrac{3}{4}\).        

B. \(F(x) = {e^x} + {x^2} + \dfrac{1}{2}\).

C. \(F(x) = {e^x} + {x^2} + \dfrac{5}{2}\).   

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

A. \(\dfrac{{146}}{{15}}\)                            

B. \(\dfrac{{116}}{{15}}\)  

C. \(\dfrac{{886}}{{105}}\)                           

D. \(\dfrac{{105}}{{886}}\) 

A. \(\cot x - 2\tan x + C\).  

B. \( - \cot x + 2\tan x + C\).

C. \(\cot x + 2\tan x + C\).  

D. \( - \cot x - 2\tan x + C\)  

A. \(\dfrac{2}{9}{\left( {{x^3} + 5} \right)^{\dfrac{3}{2}}} + C\).  

B. \(\dfrac{2}{9}{\left( {{x^3} + 5} \right)^{\dfrac{2}{3}}} + C\).

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

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

A. \(\dfrac{{2{\pi ^3}\sqrt 3 }}{{27}} + \dfrac{{{\pi ^2}}}{3} + 6 - 4\sqrt 3 \). 

B. \(\dfrac{{{\pi ^3}\sqrt 3 }}{{27}} + \dfrac{{{\pi ^2}}}{6} + 6 - 4\sqrt 3 \).

C. \(\dfrac{{2{\pi ^3}\sqrt 3 }}{{27}} + \dfrac{{{\pi ^2}}}{3} + 3 - 2\sqrt 3 \). 

D. 0.

A. \(I = \int\limits_1^0 {\left( {1 - u} \right)\,du} \)

B. \(I = \int\limits_0^1 {\left( {1 - u} \right){e^{ - u}}\,du} \).

C. \(I = \int\limits_1^0 {\left( {1 - u} \right)\,{e^{ - u}}du} \).

D. \(I = \int\limits_1^0 {\left( {1 - u} \right)\,{e^{2u}}du} \).

A. \(2\left( {{2^{\sqrt x }} - 1} \right) + C\).

B. \({2^{\sqrt x }} + C\).

C. \({2^{\sqrt x  + 1}}\).                    

D. \(2\left( {{2^{\sqrt x }} + 1} \right) + C\).

A. \(\left\{ \begin{array}{l}u = x\\dv = x\cos x\,dx\end{array} \right.\).   

B. \(\left\{ \begin{array}{l}u = {x^2}\\dv = \cos x\,dx\end{array} \right.\).

C. \(\left\{ \begin{array}{l}u = \cos x\\dv = {x^2}\,dx\end{array} \right.\). 

D. \(\left\{ \begin{array}{l}u = {x^2}\cos x\\dv = \,dx\end{array} \right.\)

A. 46        

B. 44  

C. 36 

D. 54 

A. \(I = {e^{\dfrac{\pi }{2}}} + 2\).  

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

C. \(I = {e^{\dfrac{\pi }{2}}} - 2\)       

D. \(I = {e^{\dfrac{\pi }{2}}}\). 

A. \(\dfrac{1}{3}\)    

B. 17    

C. 7    

D. 9

A. \(\int {2\sin x\,dx = {{\sin }^2}x}  + C\). 

B. \(\int {2\sin x\,dx = 2\cos x}  + C\).

C. \(\int {2\sin x\,dx =  - 2\cos x}  + C\).  

D. \(\int {2\sin x\,dx = \sin 2x}  + C\).

A. \({e^x} + 2\sin x\).     

B. \({e^x} + \sin 2x\).

C. \({e^x} + {\cos ^2}x\).  

D. \({e^x} - 2\sin x\).

A. 3 

B. 2          

C. 10 

D. 0 

A. 1         

B. 3  

C. 80            

D. 9 

A. \(I = \left. {f\left( x \right).g'\left( x \right)} \right|_a^b - \int\limits_a^b {f'\left( x \right).g\left( x \right){\rm{d}}x} .\)

B. \(I = \left. {f\left( x \right).g\left( x \right)} \right|_a^b - \int\limits_a^b {f\left( x \right).g\left( x \right){\rm{d}}x} .\)

C. \(I = \left. {f\left( x \right).g\left( x \right)} \right|_a^b - \int\limits_a^b {f'\left( x \right).g\left( x \right){\rm{d}}x} .\)

D. \(I = \left. {f\left( x \right).g'\left( x \right)} \right|_a^b - \int\limits_a^b {f\left( x \right).g'\left( x \right){\rm{d}}x} .\)

A. \({2009^x}\ln 2009\).          

B. \(\dfrac{{{{2009}^x}}}{{\ln 2009}}\).

C. \({2009^x} + 1\).                     

D. \({2009^x}\).