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

Options

A. `(5)/(3)` sq units
B. `(5)/(4)` sq units
C. `(5)/(12)` sq unit
D. `(12)/(5)` sq units

Answer

C

Explanation

Since, the intersection of two curves `y = x^(3)` and `y = sqrt(x)` are x = 0, x = 1.
`therefore A=|int_(0)^(1)(x^(3)-sqrt(x))dx|`
`=|[(x^(4))/(4)-(2x^(3//2))/(3)]_(0)^(1)|`
`=|[(1)/(4)-(2)/(3)]|=(5)/(12)` sq unit