Area bounded between the curve `x^(2)=y` and the line y = 4x is

Options

A. `(32)/(3)` sq. unit
B. `(1)/(3)` sq unit
C. `(8)/(3)` sq unit
D. `(16)/(3)` sq unit

Answer

A

Explanation

Given curves are ` x^(2)=y and y=4x`
Intersection point are ` (0,0)` and (4,16)
`:.` Required are `=int_(0)^(4) (4x-x^(2)) dx`
`=[(4x^(2))/(2)-(x^(3))/(3)]_(0)^(4)`
`=[32-(64)/(3)]`
`=(32)/(3)` sq unit