Question

Find the area of the region bounded by the curve $y^2=4x,y-axis$ & the line $y=3$.

Answer 1

Let AD represent the line $y=3$

And BOC represent the curve $y^2=4x$

We have to find area of shaded region

Area of shaded region $=$Area of AOB

$={\int }_0^{3}xdy$

We know that $y^2=4xx=\frac{y^2}{4}$

Area of shaded region $={\int }_0^{3}xdy={\int }_0^3\frac{y^2}{4}dy=\frac{1}{4}{\int }_0^3{y}^{2}dy=\frac{1}{4}[\frac{y^3}{3}{]}_0^3=\frac{1}{4}[\frac{3^3-0^3}{3}=\frac{1}{4}\left[\frac{27}{3}\right]=\frac{9}{4}$