Question

The area enclosed between the parabola $y=x^2$ and the sraight line $y=x$ is

• A. $1/8$
• B. $1/6$
• C. $1/3$
• D. $1/2$

Answer 1

The correct option is B $1/6$


Area enclosed $=\int \int \left(1\right)dydx$
$={\int }_{x=0}^1{\int }_{y=x^2}^{\left(x\right)}\left(1\right)dydx$
$={\int }_0^1(x-x^2)dx$
$={[\frac{x^2}{2}-\frac{x^3}{3}]}_0^1$
$=\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$