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Question Number 134219 by Raxreedoroid last updated on 01/Mar/21

∫_0 ^( π) cos^4  x sin x dx=?

$$\int_{\mathrm{0}} ^{\:\pi} \mathrm{cos}^{\mathrm{4}} \:{x}\:\mathrm{sin}\:{x}\:{dx}=? \\ $$

Answered by liberty last updated on 01/Mar/21

=−[(1/5)cos^5 x ]_0 ^π =−(1/5)[−1−1]=(2/5)

$$=−\left[\frac{\mathrm{1}}{\mathrm{5}}\mathrm{cos}\:^{\mathrm{5}} \mathrm{x}\:\right]_{\mathrm{0}} ^{\pi} =−\frac{\mathrm{1}}{\mathrm{5}}\left[−\mathrm{1}−\mathrm{1}\right]=\frac{\mathrm{2}}{\mathrm{5}} \\ $$

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