Find the area of the parabola `y^2=4a x`bounded by its latus rectum.

Explanation

Equation of parabola , `y^(2)=4ax`
Focus S (a,0)
Then OS =a
Latus rectum of `y^(2)=4ax` is LSL.
`y^(2)=4ax`
`rArry=2sqrt(ax)`

Area = 2 Area OSL
`=2int_(0)^(a)ydx=2int_(0)^(a)2sqrt(ax)dx`
`=4a^(1//2)int_(0)^(a)x^(1//2)dx`
`=8a^(1//2)[(x^(3//2))/(3)]_(0)^(a)`
`=8a^(1//2)xx(a^(3//2))/(3)=(8a^(2))/(3)` units