Question

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

Answer 1

The given curve is $y^2=4x,$ which represents a right hand parabola with vertex at (0, 0) and axis along X -axis and the equation of line is x = 3.

Required area $=2\times$ (Area of shaded region in the first quadrant only)

$=2{\int }_0^3|y|dx=2{\int }_0^{3}2\sqrt{x}dx(\because y^2=4x\Rightarrow y=2\sqrt{x})=4\left[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]=\frac{8}{3}[3^{\frac{3}{2}}-0]=\frac{8}{3}\left(3\sqrt{3}\right)$ sq unit