Question Number 133719 by leena12345 last updated on 23/Feb/21
![](https://www.tinkutara.com/question/19054.png)
Commented by leena12345 last updated on 23/Feb/21
![help](https://www.tinkutara.com/question/Q133721.png)
$${help} \\ $$
Answered by bramlexs22 last updated on 24/Feb/21
![V=2π∫_3 ^9 xy dy V=2π∫_3 ^9 y(1+(y−6)^2 )dy V=2π∫_3 ^9 (y+y(y−6)^2 )dy V=2π(144)=288π](https://www.tinkutara.com/question/Q133751.png)
$$\mathrm{V}=\mathrm{2}\pi\underset{\mathrm{3}} {\overset{\mathrm{9}} {\int}}\:\mathrm{xy}\:\mathrm{dy}\: \\ $$$$\mathrm{V}=\mathrm{2}\pi\underset{\mathrm{3}} {\overset{\mathrm{9}} {\int}}\mathrm{y}\left(\mathrm{1}+\left(\mathrm{y}−\mathrm{6}\right)^{\mathrm{2}} \right)\mathrm{dy} \\ $$$$\mathrm{V}=\mathrm{2}\pi\underset{\mathrm{3}} {\overset{\mathrm{9}} {\int}}\left(\mathrm{y}+\mathrm{y}\left(\mathrm{y}−\mathrm{6}\right)^{\mathrm{2}} \right)\mathrm{dy}\: \\ $$$$\mathrm{V}=\mathrm{2}\pi\left(\mathrm{144}\right)=\mathrm{288}\pi \\ $$