Cho hàm số

D

- Hướng dẫn giải

Đáp án D

Ta có:

$$\begin{gathered} F\left(x\right)=\frac{1}{2}\int \sqrt{x^2+1}d\left(x^2\right) \\ =\frac{1}{2}\int {\left(x^2+1\right)}^{\frac{1}{2}}d\left(x^2+1\right) \\ =\frac{1}{2}.\frac{{\left(x^2+1\right)}^{\frac{3}{2}}}{\frac{3}{2}}+C=\frac{1}{3}\sqrt{{\left(x^2+1\right)}^3}+C \end{gathered}$$ 

Mà $F\left(0\right)=\frac{4}{3}\Rightarrow C=1\Rightarrow F\left(2\sqrt{2}\right)=10.$