Find the area of the region bounded by the curve `y^(2)=4x" and " x^(2)=4y`.

Options

A. `15/7" sq units"`
B. `16/7" sq units"`
C. `16/3" sq units"`
D. `16" sq units"`

Answer

C

Explanation

Given wquation of curve are
`y^(2)=4x`
and `x^(2)=4y`
`rArr((x^(2))/4)=4x`
`rArr(x^(4))/4.4=4x`
`rArrx^(4)=64x`
`rArrx^(4)-64x=0`
`rArrx(x^(3)-4^(3))=0`
`rArrx=4, 0`
`"Area of shaded region",A=int_(0)^(4)(sqrt(4x)-(x^(2))/4)dx`

`=int_(0)^(4)(2sqrtx-(x^(2))/4)dx=[(x^(3//2).2)/3-1/4 .x^(3)/3]_(0)^(4)`
`=2.2/3 . 8-1/4 . 64/3-0=32/3-16/3=16/3" sq units"`