Question

The volume of the solid of revolution formed by rotating the curve $y=\sqrt[\text{n}]{\text{n}x}$ along x-axis bounded by lines $x=0$ and $x=a$ is equal to $\frac{n\pi }{n+2}{a}^{n+2/n}$.

• A. True
• B. False

Answer 1

The correct option is A True

$y=x^{1/n}$ ,$x=0$ , $x=2$

Volume of small disc $\pi y^{2}dx$

Whole volume $={\int }_0^a\pi y^{2}dx$

$={\int }_0^a\pi x^{2/n}dx$

$=\frac{\pi {\left[x^{n+2/n}\right]}_0^a}{n+2n}$

$\Rightarrow$$\frac{n\pi }{n+2}{a}^{n+2/n}$