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Category: Integration

find-the-volume-of-the-solid-formed-by-rotating-the-area-trapped-by-y-sin-x-and-the-x-axis-around-the-line-y-3-for-0-lt-x-lt-pi-

Question Number 90446 by jagoll last updated on 23/Apr/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solid} \\ $$$$\mathrm{formed}\:\mathrm{by}\:\mathrm{rotating}\:\mathrm{the}\:\mathrm{area} \\ $$$$\mathrm{trapped}\:\mathrm{by}\:\mathrm{y}\:=\:\mathrm{sin}\:\mathrm{x}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{x}−\mathrm{axis}\:\mathrm{around}\:\mathrm{the}\:\mathrm{line}\:\mathrm{y}=\mathrm{3} \\ $$$$\mathrm{for}\:\mathrm{0}<\mathrm{x}<\pi\: \\ $$ Commented by john santu last…

find-the-volume-solid-formed-by-rotating-the-area-trapped-between-the-line-y-1-and-the-function-f-x-4-3x-2-aroud-the-line-y-1-

Question Number 90443 by jagoll last updated on 23/Apr/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{solid}\:\mathrm{formed} \\ $$$$\mathrm{by}\:\mathrm{rotating}\:\mathrm{the}\:\mathrm{area}\:\mathrm{trapped} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{line}\:\mathrm{y}\:=\:\mathrm{1}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{4}−\mathrm{3x}^{\mathrm{2}} \\ $$$$\mathrm{aroud}\:\mathrm{the}\:\mathrm{line}\:\mathrm{y}\:=\:\mathrm{1} \\ $$ Commented by john santu last…

dx-1-x-12-

Question Number 90417 by jagoll last updated on 23/Apr/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{x}^{\mathrm{12}} } \\ $$ Commented by MJS last updated on 23/Apr/20 $$\mathrm{I}'\mathrm{m}\:\mathrm{afraid}\:\mathrm{you}\:\mathrm{will}\:\mathrm{have}\:\mathrm{to}\:\mathrm{find}\:\mathrm{6}\:\mathrm{square} \\ $$$$\mathrm{factors}\:\mathrm{of}\:{x}^{\mathrm{12}} +\mathrm{1}\:\mathrm{and}\:\mathrm{then}\:\mathrm{decompose}… \\…

please-prove-that-0-pi-2-log-sinx-dx-pi-2-log2-or-0-pi-2-log-cosx-dx-pi-2-log2-

Question Number 24852 by nnnavendu last updated on 27/Nov/17 $$\mathrm{please}\:\mathrm{prove}\:\mathrm{that}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{log}\left(\mathrm{sinx}\right)\mathrm{dx}=−\frac{\pi}{\mathrm{2}}\mathrm{log2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{or} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi\:\:}{\mathrm{2}}} \mathrm{log}\left(\mathrm{cosx}\right)\mathrm{dx}=−\frac{\pi}{\mathrm{2}}\mathrm{log2} \\ $$ Commented by Tinku Tara last…

Question-155919

Question Number 155919 by horpy4 last updated on 05/Oct/21 Answered by physicstutes last updated on 05/Oct/21 $$\boldsymbol{\mathrm{F}}×\boldsymbol{\mathrm{V}}\:=\:\begin{vmatrix}{{i}}&{{j}}&{{k}}\\{\mathrm{3}{u}}&{{u}^{\mathrm{2}} }&{{u}+\mathrm{2}}\\{\mathrm{2}{u}}&{−\mathrm{3}{u}}&{{u}−\mathrm{2}}\end{vmatrix}={i}\left({u}^{\mathrm{3}} −\mathrm{2}{u}^{\mathrm{2}} +\mathrm{3}{u}^{\mathrm{2}} −\mathrm{6}{u}\right) \\ $$$$−\:{j}\left(\mathrm{3}{u}^{\mathrm{2}} −\mathrm{6}{u}−\mathrm{2}{u}^{\mathrm{2}} −\mathrm{4}{u}\right)\:+\:{k}\left(−\mathrm{9}{u}^{\mathrm{2}}…