Cho $F\left( x \right) = {x^2}$ là nguyên hàm của hàm số $f\left( x \right){e^{2x}}$ và $f\left( x \right)$ là hàm số thỏa mãn điều kiện $f\left( 0 \right) =  0,\,\,f\left( 1 \right) = \dfrac{2}{e^2}.$ Tính tích phân $I = \int\limits_0^1 {f'\left( x \right){e^{2x}}{\rm{d}}x} .$

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

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

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

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

$\left\{ \begin{array}{l}u = x\\{\rm{d}}v = x\cos x\,{\rm{d}}x\end{array} \right.$

$\left\{ \begin{array}{l}u = {x^2}\\{\rm{d}}v = \cos x\,{\rm{d}}x\end{array} \right.$

$\left\{ \begin{array}{l}u = \cos x\\{\rm{d}}v = {x^2}\,{\rm{d}}x\end{array} \right.$

$\left\{ \begin{array}{l}u = {x^2}\cos x\\{\rm{d}}v = {\rm{d}}x\end{array} \right..$

 \(I = 2\)

\(I = 1\)

\(I = 3\)

\(I =  - 1\)

$8.$    

$9.$    

$24.$

$36.$

$\dfrac{{{e^2} - 1}}{2}$                                     

$\dfrac{{{e^2} + 1}}{2}$                            

$\dfrac{{{e^2} - 3}}{4}$                                 

$\dfrac{{{e^2} - 3}}{2}$

$I = \dfrac{1}{2}$

$I = \dfrac{{3{e^2} + 1}}{4}$            

$I = \dfrac{{{e^2} + 1}}{4}$

$I = \dfrac{{{e^2} - 1}}{4}$