Question

The area of the region $\{(x,y):x^2\le y\le \left|x\right|\}$ is

• A. $\left(\frac{10}{3}\right)sq.units$
• B. $2sq.units$
• C. $\left(\frac{1}{3}\right)sq.units$
• D. $noneofthese$

Answer 1

Answer: (C)

$\left(\frac{1}{3}\right)sq.units$

Area$={\int }_{0}1\times 1-x^2$

$=2[\frac{x^2}{2}-\frac{x^3}{3}]$

$=\frac{1}{3}$.