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Find the area bounded by the curve y = x...

Find the area bounded by the curve `y = x^(2) , y = (x-2)^(2)` and the axis .

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Solving `y = x^(2)` and `y = (x-2)^(2)` , we get , x = 1

The required area = `underset(0)overset(1)(int) x^(2) dx + overset(2)underset(1)(int)(x-2)^(2) dx`
`= [(x^(3))/(3)]_(0)^(1) + [((x-2)^(3))/(3)]_(1)^(2)`
`= (1)/(3) {(1 - 0) + (0 +1)}`
= `(2)/(3)` sq . units
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