Question

Find the area of the region bounded by line x = 2 and parabola $y^2=8x$.

Answer 1

We have, $y^2=8xandx=2$

$\therefore$ Area of shaded region, $A=2{\int }_0^2\sqrt{8x}dx=2.2\sqrt{2}{\int }_0^2{x}^{\frac{1}{2}}dx=4.\sqrt{2}.{\left[2.\frac{x^{\frac{3}{2}}}{3}\right]}_0^2=4\sqrt{2}[\frac{2}{3}.2\sqrt{2}-0]=\frac{32}{3}sq.units$