Question

The area bounded by the curve $y^2=4x$ and the double ordinate $x=2$, is

• A. $\frac{4}{3}\sqrt{2}$ unit${}^2$
• B. $\frac{8}{3}\sqrt{2}$ unit${}^2$
• C. $\frac{16}{3}\sqrt{2}$ unit${}^2$
• D. $\frac{32}{3}\sqrt{2}$ unit${}^2$

Answer 1

Answer: (C)

$\frac{16}{3}\sqrt{2}$ unit${}^2$

The required area
$=2{\int }_0^{2}y.dx$
$=2{\int }_0^{2}2\sqrt{x}.dx$
$=2[\frac{4x\sqrt{x}}{3}{]}_0^2$
$=2\left[\frac{8\sqrt{2}}{3}\right]$
$=\frac{16\sqrt{2}}{3}$ sq units.