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Find the area bounded by y=x^(2) and y=x...

Find the area bounded by `y=x^(2) and y=x^(1//3)" for "x in [-1,1].`

Text Solution

Verified by Experts

The correct Answer is:
`(3)/(2)` sq. units
Solving given curves we get `x^(2)=x^(1//3)`
`therefore" "x=0 or x=1`
`"Required area, "A=overset(0)underset(-1)int[x^(2)-x^(1//3)]dx+overset(1)underset(0)int[x^(1//3)-x^(2)]dx`

`=[(x^(3))/(3)-(3x^(4//3))/(4)]_(-1)^(0)+[(3x^(4//3))/(4)-(x^(3))/(3)]_(0)^(1)`
`=-[-(1)/(3)-(3)/(4)]+[(3)/(4)-(1)/(3)]=(3)/(2)` sq. units.
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