Question

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

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

Answer 1

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


$A=\underset{-4}{\overset{4}{\int }}(16-x^2)dx$

$\Rightarrow A=2\underset{0}{\overset{4}{\int }}(16-x^2)dx(\because \text{Even function})$

$\Rightarrow A=2{[16x-\frac{x^3}{3}]}_0^4$

$\Rightarrow A=2(64-\frac{64}{3})$

$\Rightarrow A=\frac{256}{3}\text{sq. units}$