MathematicsThe area of the curve y=x2 bounded by the lines x=0,x=2, and y=0 is

The area of the curve $y = x^{2}$ bounded by the lines $x = 0, x = 2,$ and $y = 0$ is

A
$\frac{4}{5}$
B
$\frac{3}{2}$
C
$\frac{3}{4}$
D
$\frac{8}{3}$

Solution:

The area of the shaded region is

$A = \int_{0}^{2} x^{2} d x = {[\frac{x^{3}}{3}]}_{0}^{2} = \frac{8}{3}$

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