Question

The area (in sq. units) of the region
$A=\text{{}(x,y):|x|+|y|\le 1,2y^2\ge |x|\text{}}$ is :

• A. $\frac{1}{3}$
• B. $\frac{7}{6}$
• C. $\frac{1}{6}$
• D. $\frac{5}{6}$

Answer 1

The correct option is D $\frac{5}{6}$

Required area $=4\left[\underset{0}{\overset{\frac{1}{2}}{\int }}2y^{2}dy+\text{area}\left(\Delta PAB\right)\right]=4[\frac{2}{3}{\left[y^3\right]}_0^{\frac{1}{2}}+\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}]=4[\frac{2}{3}\times \frac{1}{8}+\frac{1}{8}]=4\times \frac{5}{24}=\frac{5}{6}$