Cho f(2x)dx=1 và f(3x)dx=-2 . Tích phân f(x)dx bằng:

Đáp án C

Ta có $\begin{array}{l}\left\{\begin{array}{l}\underset{0}{\overset{3}{\int }}f\left(2x\right)dx=1\\ \underset{2}{\overset{4}{\int }}f\left(3x\right)dx=-2\end{array}\right.\Rightarrow \left\{\begin{array}{l}\underset{0}{\overset{6}{\int }}f\left(u\right)d\left(\frac{u}{2}\right)=1\\ \underset{0}{\overset{12}{\int }}f\left(v\right)d\left(\frac{v}{3}\right)=-2\end{array}\right.\Rightarrow \left\{\begin{array}{l}\frac{1}{2}\underset{0}{\overset{6}{\int }}f\left(u\right)du=1\\ \frac{1}{3}\underset{0}{\overset{12}{\int }}f\left(v\right)dv=-2\end{array}\right.\\ \Rightarrow \left\{\begin{array}{l}\underset{0}{\overset{6}{\int }}f\left(u\right)du=2\\ \underset{0}{\overset{12}{\int }}f\left(v\right)dv=-6\end{array}\right.\Rightarrow \left\{\begin{array}{l}\underset{0}{\overset{6}{\int }}f\left(x\right)dx=2\\ \underset{0}{\overset{12}{\int }}f\left(x\right)dx=-6\end{array}\right.\Rightarrow \underset{0}{\overset{12}{\int }}f\left(x\right)dx=\underset{0}{\overset{6}{\int }}f\left(x\right)dx+\underset{0}{\overset{12}{\int }}f\left(x\right)dx=-4\end{array}$