Question

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

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

Answer 1

The correct option is D $\frac{256}{3}sq.units$

Area$={\int }_0^{16}xdy$
$=2{\int }_0^{16}\sqrt{y}dy$
$=2\cdot \frac{2}{3}{\left|y^{3/2}\right|}_0^{16}$
$=2\cdot \frac{2}{3}[{16}^{3/2}-0]$
$=2\cdot \frac{2}{3}\cdot {\left[4\right]}^3$
$=\frac{256}{3}$ sq. units