Question

Find the area of the region bounded by the curve y2=4x and the line x=3

Answer 1

The region bounded by the parabola,y2=4x,and the line, x=3,is the area OACO.

The area OACO is symmetrical about x-axis.

∴Area of OACO=2(Area of OAB)

Area OACO=$2[∫_0^3ydx]$

=$2∫_0^3 2\sqrt{x}dx$

=$4\bigg[\frac{x\frac{3}{2}}{\frac{3}{2}}\bigg]_0^3$

=$\frac{8}{3}[(3)^\frac{3}{2}]$

$=8\sqrt3$

Therefore,the required area is $8\sqrt3$units.