Question

The area of the region bounded by the curves, $y^2=8x$ and $y=x$ is

• A. $\frac{64}{3}$
• B. $\frac{32}{3}$
• C. $\frac{16}{3}$
• D. $\frac{8}{3}$

Answer 1

Answer: (B)

$\frac{32}{3}$

Given curves,

$y^2=8x\to$ (i)

and $y=x\to$ (ii)

On solving Eqs. (i) and (ii), we get

$x^2-8x=0$

$x(x-8)=0$

and $y=0,8$

$\therefore$ Required area (OPA) $={\int }_0^8(\sqrt{8x}-x)dx$

$={[2\sqrt{2}.\frac{2}{3}.x^{3/2}-\frac{x^2}{2}]}_0^8$

$=\frac{4\sqrt{2}}{3}.(8{)}^{3/2}-\frac{8^2}{2}$

$=\frac{32}{3}$