Question

Find the area of the region enclosed by the parabola $x^2$ = $y$, the line $y=x+2$ and the $x$- axis

Answer 1

Shaded area$={\int }_{-2}^{-1}(x+2)dx+{\int }_{-1}^0{x}^{2}dx$

$={[\frac{x^2}{2}+2x]}_{-2}^{-1}+{\left[\frac{x^3}{3}\right]}_{-1}^0$

$=\frac{1}{2}-2-2+4+\frac{1}{3}=\frac{5}{6}$