The area enclosed between the curves `y = x^(3)` and `y = sqrt(x)` is

Options

A. `5/3`
B. `5/4`
C. `5/12`
D. None of these

Answer

C

Explanation

The curve `y=sqrt(x)` is
`y^(2)=x,(yge0)`……………i
Points of intersection of the curves
(1) and curve
`y=x^(3)`………….ii
are (0,0) and (1,1)

`:.` Required area `=int_(0)^(1)(y_(1)-y_(2))dx`
`=int_(0)^(1) (sqrt(x)-x^(3))dx`
`=5/12`