Question Number 170996 by Mastermind last updated on 06/Jun/22
![Find the volume of the solid obtained by rotating about x−axis of the curve y=(√x) on the interval [0, 2]. Mastermind](https://www.tinkutara.com/question/Q170996.png)
$${Find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\:{obtained} \\ $$$${by}\:{rotating}\:{about}\:{x}−{axis}\:{of}\:{the}\:{curve} \\ $$$${y}=\sqrt{{x}}\:{on}\:{the}\:{interval}\:\left[\mathrm{0},\:\mathrm{2}\right]. \\ $$$$ \\ $$$${Mastermind} \\ $$
Answered by mr W last updated on 06/Jun/22
$${Method}\:{I}: \\ $$$${V}=\mathrm{2}\pi×\frac{\mathrm{2}×\mathrm{2}×\sqrt{\mathrm{2}}}{\mathrm{3}}×\frac{\mathrm{3}\sqrt{\mathrm{2}}}{\mathrm{8}}=\mathrm{2}\pi \\ $$$$ \\ $$$${Method}\:{II}: \\ $$$${V}=\pi\int_{\mathrm{0}} ^{\mathrm{2}} {y}^{\mathrm{2}} {dx}=\pi\int_{\mathrm{0}} ^{\mathrm{2}} {xdx}=\frac{\pi}{\mathrm{2}}\left(\mathrm{2}^{\mathrm{2}} −\mathrm{0}^{\mathrm{2}} \right)=\mathrm{2}\pi \\ $$