Question

The area (in square units) of the region bounded by the parabolas $y^2=6x\mathrm{and}{x}^2=6y$ is

Answer 1

The intersecting points of the given parabolas are obtained by solving these equations for x and y, which are 0(0, 0) and (6, 6).
Hence,
Area OABC =
${\int }_0^6\left(\sqrt{6x}-\frac{x^2}{6}\right)\mathrm{dx}={\left(2\sqrt{6}\frac{x^{\frac{3}{2}}}{3}-\frac{x^3}{18}\right]}_0^6=2\sqrt{6}\frac{6^{\frac{3}{2}}}{3}-\frac{6^3}{18}=24-12=12\mathrm{square}\mathrm{units}$