The area (in s units) of the region (\\{ (x , y) : x \>= 0 ,... | Mathematics | SolveeIt | Solveeit

Today, August 18

Question

The area (in s 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

A

$\frac{3}{2}$

B

$\frac{7}{3}$

C

$\frac{5}{2}$

D

$\frac{59}{12}$

Answer

$\frac{5}{2}$

Explanation

Solution

Area of shaded region
$= \int\limits^{1}_{0}$ $\left(\sqrt{x}+1-\frac{x^{2}}{4}\right)dx+$ $= \int\limits^{2}_{1}$ $\left(\left(3-x\right)-\frac{x^{2}}{4}\right)dx$
$= \frac{5}{2 }$ s unit