The area bounded by the parabola $y=x^2$ and the line $y=x$ is

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Aicharya · Accepted Answer

The required area is shaded The point of intersection of the curves are $x^2=x \Rightarrow x(x-1)=0$ i.e. $O(0,0)$ and $P(1,1)$ $\begin{aligned} & 	herefore A=\int_0^1\left(x-x^2ight) d x \ & =\left[\frac{x^2}{2}ight]_0^1-\left[\frac{x^3}{3}ight]_0^1=\frac{1}{2}-\frac{1}{3}=\frac{1}{6} \end{aligned}$

The area bounded by the parabola $y=x^2$ and the line $y=x$ is

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