Question

Find the area of the region bounded by the parabola $y^2=16x$ and the line $x=3$.

Answer 1

Equation of the parabola is
$y^2=16x$ .... (i)
Required area $=2{\int }_0^{3}ydx$
[by symmetry about $x$-axis]
$=2{\int }_0^{3}4\sqrt{x}dx$
$=8{\int }_0^3{x}^{\frac{1}{2}}dx$
$=8{\left(\frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right)}_0^3$
$=\frac{16}{3}\left(3\sqrt{3}\right)$
$=16\sqrt{3}$ square units.