Question

The area bounded by the curve $x^2=4y$, $x-$ axis and the line $x=2$ is

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

Answer 1

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

Given $y=\frac{x^2}{4}$

$A=\underset{0}{\overset{2}{\int }}\frac{x^2}{4}dx$
$A=\frac{1}{4}{\left[\frac{x^3}{3}\right]}_0^2$
$A=\frac{1}{4}\left(\frac{8}{3}\right)$
$A=\frac{2}{3}$ sq. units