Cho hàm số

C

- Hướng dẫn giải

Đáp án C

Đặt $t=x-1\Rightarrow dx=dt$ và $\left\{\begin{array}{l}x=1\Rightarrow t=0\\ x=2\Rightarrow t=1\end{array}\right..$ Khi đó $\underset{1}{\overset{2}{\int }}f\left(x-1\right)dx=\underset{0}{\overset{1}{\int }}f\left(t\right)dt=3\Rightarrow \underset{0}{\overset{1}{\int }}f\left(x\right)dx=3$

Đặt $\left\{\begin{array}{l}u=x\\ dv=f\text{'}\left(x\right)dx\end{array}\right.\iff \left\{\begin{array}{l}du=dv\\ v=f\left(x\right)\end{array}\right.$ suy ra $\underset{0}{\overset{1}{\int }}x.f\text{'}\left(x\right)dx={\left.x.f\left(x\right)\right|}_0^1-\underset{0}{\overset{1}{\int }}f\left(x\right)dx=f\left(1\right)-\underset{0}{\overset{1}{\int }}f\left(x\right)dx=-1$