Question

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

• A. $\frac{32}{3}$ sq. units
• B. $\frac{16}{3}$ sq. units
• C. $\frac{8}{3}$ sq. units
• D. $\frac{4}{3}$ sq. units

Answer 1

Answer: (A)

$\frac{32}{3}$ sq. units

Symmetric about x-axis
So, area is
$2\stackrel{4}{\underset{0}{\int }}ydx$
$2\stackrel{4}{\underset{0}{\int }}\sqrt{x}dx$
$2\times \frac{2}{3}(2^3-0)=\frac{32}{3}squnits$