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

A. 11     

B. 9    

C. 7      

D. 12,5.

A. 1 – ln2                    

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

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

D. \(3 - 2\ln 2\).

A. \(\int\limits_a^b {v.du = u.v\left| \begin{array}{l}b\\a\end{array} \right. - \int\limits_a^b {u.dv} } \).            

B. \(\int\limits_a^b {u.dv = u.v\left| \begin{array}{l}b\\a\end{array} \right. + \int\limits_a^b {v.du} } \).

C. \(\int\limits_a^b {u.dv = u.v\left| \begin{array}{l}b\\a\end{array} \right. - \int\limits_a^b {v.du} } \).       

D. \(\int\limits_a^b {u.dv = u.v\left| \begin{array}{l}b\\a\end{array} \right. - \int\limits_a^b {u.dv} } \)

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

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

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

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

A. \(dt = \dfrac{{v(x)}}{{u(t)}}dx\)               

B. \(dt = \dfrac{{v'(x)}}{{u'(t)}}dx\)

C. \(dx = \dfrac{{v(x)}}{{u(t)}}dt\)           

D. \(dx = \dfrac{{v'(x)}}{{u'(t)}}dt\).

A. \(\int {\left( {\dfrac{1}{{{{\sin }^2}x}} + \dfrac{1}{{{{\cos }^2}x}}} \right)dx = \tan x - \cot x + C} \)

B. \(\int {\left( {\dfrac{1}{{{{\sin }^2}x}} + \dfrac{1}{{{{\cos }^2}x}}} \right)dx =  - \tan x + \cot x + C} \).

C. \(\int {\left( {\dfrac{1}{{{{\sin }^2}x}} + \dfrac{1}{{{{\cos }^2}x}}} \right)dx = \tan x + \cot x + C} \).

D. \(\int {\left( {\dfrac{1}{{{{\sin }^2}x}} + \dfrac{1}{{{{\cos }^2}x}}} \right)dx =  - \tan x - \cot x + C} \).

A. f’(x) = F(x)           

B. \(\int {f(x)dx = F(x) + C} \)

C. \(\int {F(x)dx = f(x) + C} \)      

D. f’(x) = F’(x).

A. \(I = \dfrac{1}{4}\ln \left| {\dfrac{{x - 2}}{{x + 2}}} \right|\)   

B. \(I = \dfrac{1}{2}\ln \left| {\dfrac{{x + 2}}{{x - 2}}} \right|\).

C. \(I = \dfrac{1}{4}\ln \left| {\dfrac{{x + 2}}{{x - 2}}} \right|\).      

D. \(I = \dfrac{1}{2}\ln \left| {\dfrac{{x - 2}}{{x + 2}}} \right|\)

A. six2x + C .                    

B. –cosx – sinx + C

C. cosx + sinx + C.                

D. sinx – cosx + C.

A. a = 2      

B. a = -2  

C. a = 1     

D. a = 0.

A. \(\dfrac{{202}}{3}\)      

B. \(\dfrac{{203}}{4}\)    

C. \(\dfrac{{201}}{5}\)    

D. \(\dfrac{{201}}{4}\).

A. \(I = \dfrac{1}{5}{e^{3 - 5x}} + C\).   

B. \(I =  - \dfrac{1}{5}{e^{3 - 5x}} + C\).

C. \(I = {e^{3 - 5x}} + C\).     

D. \(I =   \dfrac{1}{5}{e^{3 - 5x}} + C\).

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

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

C. \(\int {\dfrac{1}{{{x^2}\,}}\,dx}  =  - \dfrac{1}{x} + C\,\,\,(x \ne 0)\)   

D. \(\int {{a^x}\,dx}  = {a^x} + C\).

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

B. \(I = \left( {1 - \dfrac{\pi }{2}} \right)\cos a - \sin a\).

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

D. \(I = \left( {\dfrac{\pi }{2} + 1} \right)\cos a - \sin a\).

A. \(\int\limits_{ - 1}^1 {dx = 1} \).

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

C. Nếu f(x) liên tục và không âm trên đoạn [a ; b] thì \(\int\limits_a^b {f(x)\,dx \ge 0} \).

D. Nếu \(\int\limits_a^b {f(x)\,dx = 0} \) với \(a \ne b\) thì \(f(x) = 0\).

A. \(\int {\dfrac{1}{{{{\cos }^2}x}}dx = \tan x + C} \).   

B. \(\int {\dfrac{1}{{{{\sin }^2}x}}dx = \cot x + C} \).

C. \(\int {\dfrac{1}{{{{\sin }^2}x}}dx =  - \cot x + C} \). 

D \(\int {\dfrac{1}{{{{\cos }^2}x}}} dx = \dfrac{{\sin x}}{{\cos x}} + C\)

A. \(\int {0dx = C} \)      

B. \(\int {dx = C} \)

C. \(\int {dx}  = 0\)           

D. \(\int {0dx = x + C} \).

A. \(V = \pi \int\limits_a^b {|f(x)|\,dx} \).    

B. \(V = \int\limits_a^b {|f(x)|\,dx} \).

C. \(V = \pi \int\limits_a^b {{f^2}(x)} \,dx\).  

D. \(V = {\pi ^2}\int\limits_a^b {{f^2}(x)\,dx} \).

A. \(F(x) =  - 3\cos x + 2\ln |x| + C\).

 B. \(F(x) = 3\cos x + 2\ln |x| + C\).

C. \(F(x) =  - 3\cos x - 2\ln |x| + C\).  

D. \(F(x) = 3\cos x - 2\ln |x| + C\).

A. \(\left| {\int\limits_{ - 2}^1 {\left( {{x^3} - x} \right)\,dx} } \right|\).    

B. \(\int\limits_{ - 2}^1 {\left( {{x^3} - x} \right)\,dx} \).

C. \(\int\limits_{ - 1}^1 {|{x^3} - x|\,dx} \).  

D. \(\int\limits_{ - 2}^1 {|{x^3} - x|\,dx} \).

A.\(\int\limits_0^\pi  {\cos (3x + \pi )\,dx} \).    

B. \(3\int\limits_0^{3x} {\sin x\,dx} \)

C. \(\int\limits_0^2 {\left( {{x^2} + x - 3} \right)} \,dx\).

D. \(\int\limits_0^{\ln \sqrt {10} } {{e^{2x}}} \,dx\).

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

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

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

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

A. \(\dfrac{8}{3}\)      

B. \(\dfrac{7}{3}\)      

C. \(\dfrac{9}{2}\)   

D. \(\dfrac{{10}}{3}\)

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

B. \(\dfrac{{{x^2}}}{2} - \dfrac{1}{x} - \dfrac{1}{2}\). 

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

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

A. \(I = \dfrac{{{x^5}}}{5} + {x^3} + C\)         

B. \(I = \dfrac{{{x^5}}}{5} + {x^3}\)

C.  \(I = \left( {\dfrac{{{x^3}}}{3} + 3x} \right)\dfrac{{{x^3}}}{3} + C\)     

D. \(I = {x^4} + 3{x^2} + C\).