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

A.\(\frac{1}{2}\)

B. \(\frac{1}{4}\)

C. 1

D. 0

A.S=0

B.S=1

C.\[S = \frac{1}{2}\]

D. \[S = \frac{3}{8}\]

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

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

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

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

A.\(\left\{ {\begin{array}{*{20}{c}}{u = x}\\{dv = xcosxdx}\end{array}} \right.\)

B. \(\left\{ {\begin{array}{*{20}{c}}{u = {x^2}}\\{dv = cosxdx}\end{array}} \right.\)

C. \(\left\{ {\begin{array}{*{20}{c}}{u = cosx}\\{dv = {x^2}dx}\end{array}} \right.\)

D. \(\left\{ {\begin{array}{*{20}{c}}{u = {x^2}cosx}\\{dv = dx}\end{array}} \right.\)

A.\[I = \frac{1}{2}\]

B. \[I = \frac{{3{e^2} + 1}}{4}\]

C. \[I = \frac{{{e^2} + 1}}{4}\]

D. \[I = \frac{{{e^2} - 1}}{4}\]

A.\[\frac{{32}}{{15}}\]

B. \[\frac{{86}}{{15}}\]

C. \[\frac{{ - 11}}{{15}}\]

D. \[\frac{{16}}{{15}}\]