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.