Question

The area in square units of the region bounded by the curve $x^2=4y$, the line $x=2$ and the X-axis is:

• A. 1
• B. $\frac{2}{3}$
• C. $\frac{4}{3}$
• D. $\frac{8}{3}$

Answer 1

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

$x^2=4y;x=2$
Area $=\stackrel{2}{\underset{0}{\int }}\frac{x^2}{4}dx$
$=\frac{1}{4}\left(\frac{x^3}{3}\right){|}_0^2$

$=\frac{8}{3}\times \frac{1}{4}=\frac{2}{3}$