Question

The area bounded by the parabolas $y^2=4x$ and $x^2=4y$ is

• A. $\frac{8}{3}$
• B. $\frac{16}{3}$
• C. $\frac{20}{3}$
• D. $\frac{32}{3}$

Answer 1

The correct option is B $\frac{16}{3}$


Point of contact of both the parabolas
$x^2=4\times 2\sqrt{x}\Rightarrow x=4$
Area bounded by the parabolas will be
$=\underset{0}{\overset{4}{\int }}2\sqrt{x}-\frac{x^2}{4}dx={[2\frac{x^{3/2}}{3/2}-\frac{x^3}{12}]}_0^4=\frac{4}{3}\times 8-\frac{64}{12}=\frac{32}{3}-\frac{16}{3}=\frac{16}{3}$