# Science talk:Math Exam Resources/Courses/MATH101/April 2017/Question 05 (a)

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Add new solution005:48, 3 March 2018
Add new solution005:48, 3 March 2018

## Add new solution

In my opinion, using substitution makes the answer more simple. Also, I guess many students first think about substitution ${\displaystyle u=\cos x}$ for

${\displaystyle \int _{0}^{\pi }\sin ^{5}xdx=\int _{0}^{\pi }\sin ^{4}x\sin xdx-\int _{0}^{\pi }(1+\cos ^{2}x)^{2}\sin xdx}$,

instead of using integration by parts.

If you agree, can you move the current solution to the second solution, and write the first hint and solution based on substitution?

05:48, 3 March 2018