Find the area of the region bounded by the parabola `y=x^2` and `y=|x|`.

Explanation

`{y}=|{x}| cdots(2)`


Curve (i) is symmetrical about `{y}`-axis since it contains even power of `{x}`.


Solving (1) and (2), we get


Case 1: If `x geq 0, x^{2}=x Rightarrow x(x-1)=0`


Therefore, `{x}=0, {x}=1`


So, the point os intersections are `(0,0)` and `(1,1)`


Case 2: If `{x} leq 0, {x}^{2}=-{x} Rightarrow {x}({x}+1)=0`


Therefore `{x}=0, {x}=-1`


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