Question

The area of the region bounded by the curve $y=x^2$ and the line $y=16$ is

• A. $\frac{32}{3}$ sq. units
• B. $\frac{256}{3}$ sq. units
• C. $\frac{64}{3}$ sq. units
• D. $\frac{128}{3}$ sq. units

Answer 1

Answer: (B)

According to the question ,

Required area$=2\underset{0}{\overset{16}{\int }}xdy$
$=2\underset{0}{\overset{16}{\int }}\sqrt{y}dy$
$=2{\left[\frac{y^{3/2}}{3/2}\right]}_0^{16}$
$=\frac{4}{3}\left[16^{3/2}-0^{3/2}\right]$
$=\frac{4}{3}\times 64=\frac{256}{3}$ sq units.