Question

Area lying between the curves $y^2=2x$ and $y=x$ is:

• A. $\frac{2}{3}$ sq. units
• B. $\frac{1}{3}$ sq. units
• C. $\frac{1}{4}$ sq. units
• D. $\frac{3}{4}$ sq. units

Answer 1

The correct option is A $\frac{2}{3}$ sq. units

First solve both the curves, $y^2=2x$ and $y=x$

$\Rightarrow x^2=2x\Rightarrow x=0$ or $x=2$

Thus required area $=$ shaded region $={\int }_0^2(x^2-x)dx$

$={[\frac{x^3}{3}-\frac{x^2}{2}]}_0^2=\frac{8}{3}-2=\frac{2}{3}$, sq. units