Thi online: 50 bài toán nguyên hàm - Mức độ 2: Thô...

A \(\int {f\left( x \right)dx = {x^3} + {e^{ - x}} + C} \)

B \(\int {f\left( x \right)dx = {x^3} - {e^{ - x}} + C} \)                                        

C \(\int {f\left( x \right)dx = {x^2} - {e^{ - x}} + C} \)

D \(\int {f\left( x \right)dx = {x^3} - {e^x} + C} \)

A \(\frac{{23}}{{252}}\).

B \(\frac{{241}}{{252}}\).

C \(\frac{{52}}{9}\).   

D \(\frac{7}{9}\).

A \(F\left( {\frac{\pi }{8}} \right) - F(0) =  1\)

B \(F\left( {\frac{\pi }{8}} \right) - F(0) = \frac {1}{4}\)

C \(F\left( {\frac{\pi }{8}} \right) - F(0) =  - 1\)

D \(F\left( {\frac{\pi }{8}} \right) - F(0) = \frac{ - 1}{4}\)

A \(\int\limits_a^b {F'\left( x \right)} dx = \sin b - \sin a\)

B \(\int\limits_a^b {F'\left( x \right)} dx = - \left( {\sin b - \sin a} \right)\)

C \(\int\limits_a^b {F'\left( x \right)} dx = - \left( {\cos b - \cos a} \right).\)

D \(\int\limits_a^b {F'\left( x \right)} dx =\cos b - \cos a\)

A        \(F\left( x \right) =  - \cos x + {e^x} - \dfrac{5}{2}{x^2} + 1\)

B        \(F\left( x \right) = \cos x + {e^x} - 5x + 3\)

C        \(F\left( x \right) = \cos x + {e^x} - \dfrac{5}{2}{x^2}\)                                  

D \(F\left( x \right) =  - \cos x + \dfrac{{{e^x}}}{{x + 1}} - \dfrac{5}{2}{x^2}\)

A        \(f\left( x \right) = \sqrt x  + \ln x\)                         

B        \(f\left( x \right) = \dfrac{{x - 1}}{{{x^2}}}\)

C        \(f\left( x \right) =  - \sqrt x  + \dfrac{1}{x} + \ln x\)

D        \(f\left( x \right) = \dfrac{{ - 1}}{{{x^2}}} + \ln x\)

A  \(\int {f\left( {5x} \right)\,{\rm{d}}x = \dfrac{4}{5}x\ln \left( {10x + 1} \right) + C} .\)    

B  \(\int {f\left( {5x} \right)\,{\rm{d}}x = 4x\ln \left( {10x + 5} \right) + C} .\)                          

C \(\int {f\left( {5x} \right)\,{\rm{d}}x = 20x\ln \left( {10x + 1} \right) + C} .\)                         

D  \(\int {f\left( {5x} \right)\,{\rm{d}}x = 4x\ln \left( {10x + 1} \right) + C} .\)

A \(F\left( x \right) =  - \left( {x + 1} \right){e^{ - x}} + 1\)                                                   

B \(F\left( x \right) = \left( {x + 1} \right){e^{ - x}} + 2\).

C \(F\left( x \right) = \left( {x + 1} \right){e^{ - x}} + 1\).                          

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