Question

Find the area of the region bounded by the parabola $y^2=4ax$ and its latus rectum.

Answer 1

required area $=2{\int }_0^{a}vdx=2{\int }_0^{a}2\sqrt{a}\sqrt{x}dx$

$=4\sqrt{a}{\left[\frac{x^{3/2}}{3/2}\right]}_0^a$

$=\frac{8\sqrt{a}}{3}.a^{3/2}$

$=\frac{8}{3}{a}^2$ sq. unit