Question

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

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

Answer 1

Answer: (A)

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