Cho hàm số y = f(x) 

A

- Hướng dẫn giải

Đáp án A

Đặt $t=\sqrt{x}\iff dt=\frac{dx}{2\sqrt{x}}\iff dx=2dt;\left\{\begin{array}{l}x=0\Rightarrow t=0\\ x=4\Rightarrow t=2\end{array}\right.$ 

Khi đó $I={\int }_0^{4}f\text{'}\left(\sqrt{x}\right)dx={\int }_0^{2}2t.f\text{'}\left(t\right)dt=2{\int }_0^{2}t.f\text{'}\left(t\right)dt$ 

Đặt $\left\{\begin{array}{l}u=t\\ dv=f\text{'}\left(t\right)dt\end{array}\right.\iff \left\{\begin{array}{l}du=dt\\ v=f\left(t\right)\end{array}\right.\Rightarrow 2{\int }_0^{2}t.f\text{'}\left(t\right)dt=t.{\overline{)f\left(t\right)}}_0^2-{\int }_0^{2}f\left(t\right)dt=2f\left(2\right)-1=-5$

Vậy tích phân $I=2.\left(-5\right)=-10$.