Question

Find the area of the region bounded by the curve $y^2=4x$ and $x=3$ ?

Answer 1

Let AB represents the line $x=3$ and AOB represent the curve $y^2=4x$.

Area of AOBC = $2\times ar\left(AOC\right)$

$=2\times \underset{0}{\overset{3}{\int }}ydx$

We know,

$y^{=}4x$

$y=\pm 2\sqrt{x}$

As AOC is in 1st quadrant, $y=2\sqrt{x}$

Therefore, area of AOBC = $2\times \underset{0}{\overset{3}{\int }}2\sqrt{x}dx$

$=4\underset{0}{\overset{3}{\int }}\sqrt{x}dx$

$=\frac{8}{3}[3^{3/2}-0]$

$=8\sqrt{3}$

Therefore, required area = $8\sqrt{3}sq.units$