Question

Area bounded between the curve $x^2=y$ and the line $y=4x$ is

• A. $\frac{32}{3}$sq unit
• B. $\frac{1}{3}$sq unit
• C. $\frac{8}{3}$sq unit
• D. $\frac{16}{3}$sq unit

Answer 1

The correct option is A $\frac{32}{3}$sq unit

Given curves are $x^2=y$ and $y=4x$
Intersection points are $(0,0)$ and $(4,16)$
$\therefore$ Required area $={\int }_0^4(4x-x^2)dx$
$={\left[\frac{4x^2}{2}-\frac{x^3}{3}\right]}_0^4$
$=[32-\frac{64}{3}]$
$=\frac{32}{3}$sq unit