Question Number 133719 by leena12345 last updated on 23/Feb/21
Commented by leena12345 last updated on 23/Feb/21
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Answered by bramlexs22 last updated on 24/Feb/21
$$\mathrm{V}=\mathrm{2}\pi\underset{\mathrm{3}} {\overset{\mathrm{9}} {\int}}\:\mathrm{xy}\:\mathrm{dy}\: \\ $$$$\mathrm{V}=\mathrm{2}\pi\underset{\mathrm{3}} {\overset{\mathrm{9}} {\int}}\mathrm{y}\left(\mathrm{1}+\left(\mathrm{y}−\mathrm{6}\right)^{\mathrm{2}} \right)\mathrm{dy} \\ $$$$\mathrm{V}=\mathrm{2}\pi\underset{\mathrm{3}} {\overset{\mathrm{9}} {\int}}\left(\mathrm{y}+\mathrm{y}\left(\mathrm{y}−\mathrm{6}\right)^{\mathrm{2}} \right)\mathrm{dy}\: \\ $$$$\mathrm{V}=\mathrm{2}\pi\left(\mathrm{144}\right)=\mathrm{288}\pi \\ $$