Cho hình D giới hạn bởi c...

B

- Hướng dẫn giải

Đáp án B

Xét phương trình:  

$\begin{array}{l}{x}^2-2=-\left|x\right|\\ \iff \left\{\begin{array}{l}-x^2+2\ge 0\\ \left[\begin{array}{l}{x}^2-2=-x\\ x^2-2=x\end{array}\right.\end{array}\right.\\ \iff \left\{\begin{array}{l}\sqrt{2}\le x\le 2\\ \left[\begin{array}{l}{x}^2+x-2=0\\ x^2-x-2=0\end{array}\right.\end{array}\right.\iff x=\pm 1\end{array}$

Đồ thị hàm số $y=x^2-2$ và $y=-\left|x\right|=\left\{\begin{array}{l}x\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}khi\hspace{0.17em}\hspace{0.17em}}x<0\\ -x\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}khi\hspace{0.17em}\hspace{0.17em}}x\ge 0\end{array}\right.$

$\Rightarrow S=\underset{-1}{\overset{0}{\int }}\left[x-\left(x^2-2\right)\right]dx$$+\underset{0}{\overset{1}{\int }}\left[-x-\left(x^2-2\right)\right]dx=\frac{7}{3}$