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Question
Solution
\[Let\ I = \int_0^\pi \cos^5 x d x\]
\[ = \int_0^\pi \cos x \left( \cos^2 x \right)^2 dx\]
\[ = \int_0^\pi \cos x \left( 1 - \sin^2 x \right)^2 dx\]
\[ Let \sin x = t, then\ \cos x\ dx = dt\]
\[When\, x \to 0 ; t \to 0\ and\ x \to \pi ; t \to 0\]
\[ \text{Therefore}, \]
\[I = \int_0^0 \left( 1 - t^2 \right)^2 dt\]
\[ = 0\]
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