Question

Area bounded by the curve $y=x^2$ and lines $x=4$ and $y=0$ is given by,

• A. $64$
• B. $\frac{64}{3}$
• C. $\frac{128}{3}$
• D. $\frac{128}{4}$

Answer 1

The correct option is B $\frac{64}{3}$

$y=x^2,x=4$ and $y=0$



Shaded area required is

$={\int }_{x=0}^4{\int }_{y=0}^{x^2}\left(1\right)dydx$
$={\int }_0^4{x}^{2}dx={\left[\frac{x^3}{3}\right]}_0^4=\frac{64}{3}sq.units$