The area of the region bounded by the curves `y^(2)=8x` and y = x (in sq unit) is

Options

A. `(64)/(3)`
B. `(32)/(3)`
C. `(16)/(3)`
D. `(8)/(3)`

Answer

B

Explanation

Given curves, `y^(2)=8x" … (i)"`
and `y = x" … (ii)"`

On solving Eqs. (i) and (ii) we get `x^(2)-8x=0`
`x(x-8)=0rArrx=0, 8 andy =0,8`
`therefore` Required area, (OPA) `=int_(0)^(8)(sqrt(8x)-x)dx`
`=[2sqrt(2).(2)/(3).x^(3//2)-(x^(2))/(2)]_(0)^(8)=(4sqrt(2))/(3).(8)^(3//2)-((8)^(2))/(2)`
`=(4sqrt(2))/(3).(2)^(3).2sqrt(2)-(64)/(2)=(16)/(3)xx8-(64)/(2)=64((2)/(3)-(1)/(2))`
`=64xx((4-3))/(6)=64xx(1)/(6)=(32)/(3)`