Question

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

• A. $\frac{16}{3}$ sq. units
• B. $\frac{64}{3}$ sq. units
• C. $7\sqrt{2}$ sq. units
• D. none of these

Answer 1

Answer: (B)

We have, $y^2=x$ a parabola with vertex $(0,0)$ and line $y=4$

Required area = area of shaded region
$A=\underset{0}{\overset{4}{\int }}{y}^{2}dy={\left[\frac{y^3}{3}\right]}_0^4=\frac{64}{3}$ sq. units