Question

The area of the closed figure bounded by $x=-1,x=2$ and $y=\{\begin{array}{cc}-x^2+2& x\le 1\\ 2x-1,& x>1\end{array}$ and the x-axis is

• A. $\frac{16}{3}$ sq. units
• B. $\frac{10}{3}$ sq. units
• C. $\frac{13}{3}$ sq. units
• D. $\frac{7}{3}$ sq. units

Answer 1

The correct option is B $\frac{10}{3}$ sq. units

By the graph
$A={\int }_{-1}^1(-x^2+1)+{\int }_1^2(2x-1)dx$