Question

The area of the region bounded by the curve $y=x^2,x$-axis and the ordinates $x=0,x=2$ is:

• A. $\frac{8}{3}$ sq. units
• B. $\frac{3}{8}$ sq. units
• C. $24$ sq. units
• D. $25$ sq. units

Answer 1

The correct option is A $\frac{8}{3}$ sq. units

$y=x^2$
$\Rightarrow$ area is the shaded region
$\stackrel{2}{\underset{0}{\int }}{x}^{2}dx=\frac{x^3}{3}{|}_0^2$
$=\frac{8}{3}squnits$.