Question Number 134219 by Raxreedoroid last updated on 01/Mar/21
$$\int_{\mathrm{0}} ^{\:\pi} \mathrm{cos}^{\mathrm{4}} \:{x}\:\mathrm{sin}\:{x}\:{dx}=? \\ $$
Answered by liberty last updated on 01/Mar/21
![=−[(1/5)cos^5 x ]_0 ^π =−(1/5)[−1−1]=(2/5)](https://www.tinkutara.com/question/Q134220.png)
$$=−\left[\frac{\mathrm{1}}{\mathrm{5}}\mathrm{cos}\:^{\mathrm{5}} \mathrm{x}\:\right]_{\mathrm{0}} ^{\pi} =−\frac{\mathrm{1}}{\mathrm{5}}\left[−\mathrm{1}−\mathrm{1}\right]=\frac{\mathrm{2}}{\mathrm{5}} \\ $$