Q. The area (in sq. units) of the region $\{ (x , y) : x \geq 0 , x + y \leq 3, x^2 \leq 4 y$ and $y \leq 1 + \sqrt{x} \}$ is
Solution:
Area of shaded region
$= \int\limits^{1}_{0}$$\left(\sqrt{x}+1-\frac{x^{2}}{4}\right)dx+ $$= \int\limits^{2}_{1}$$\left(\left(3-x\right)-\frac{x^{2}}{4}\right)dx$
$= \frac{5}{2 }$ sq. unit
