Question

Using integration, find the area of the region bounded by the line $x+2=y,$ the curve $x=\sqrt{y}$ and $y$ -axis.

Answer 1

$\begin{array}{c}Areaofshadedpart=\\ {\int }_0^2\left(x+2\right)dx-{\int }_0^2{x}^{2}dx\\ ={\left[\frac{x^2}{2}+2x\right]}_0^2-{\left[\frac{x^3}{3}\right]}_0^2\\ =\frac{10}{3}unitsq.\end{array}$