Find the area bounded by curves `{(x ,y):ygeqx^2 and y = | x |}`

Explanation

The given curve is `{(x ,y):ygeqx^2 and y = | x |}`
shaded region is
It can be observed that the required area is symmetrical about y-axis.
Required area = `2[ Area (OCAO)- Area (OCADO)]`
`= 2[ int_0^1 x dx - int_0^1 (x^2) dx]`
=` 2[ (x^2/2)_0^1 -(x^3/3)_0^1] `
=`2[ 1/(2) - 1/3]` = `2[1/6]` = `1/3` sq. units