Câu hỏi 30

Đặt \(t = 6x \Rightarrow dt = 6dx \Rightarrow dx = \dfrac{{dt}}{6}\).

Khi đó \(1 = \int\limits_0^1 {xf\left( {6x} \right)dx}  = \int\limits_0^6 {\dfrac{1}{6}t.f\left( t \right).\dfrac{{dt}}{6}}  = \dfrac{1}{{36}}\int\limits_0^6 {t.f\left( t \right)dt} \) \( \Rightarrow \int\limits_0^6 {xf\left( x \right)dx}  = 1.36 = 36\).

Đặt \(\left\{ \begin{array}{l}{x^2} = u\\f'\left( x \right)dx = dv\end{array} \right. \Rightarrow \left\{ \begin{array}{l}du = 2xdx\\v = f\left( x \right)\end{array} \right.\)

\( \Rightarrow \int\limits_0^6 {{x^2}f'\left( x \right)dx}  = \left. {{x^2}f\left( x \right)} \right|_0^6 - \int\limits_0^6 {2xf\left( x \right)dx}  = 36f\left( 6 \right) - 2\int\limits_0^6 {xf\left( x \right)dx}  = 36.1 - 2.36 =  - 36\).

Chọn D.