Bài tập 64 trang 178 SGK Toán 12 NC

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.