Problem

Evaluate $\int_{\pi}^{\pi} \sin ^{2}(x) \cos ^{4}(x) d x$

Answer

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Answer

Final Answer: The value of the integral \(\int_{\pi}^{\pi} \sin ^{2}(x) \cos ^{4}(x) d x\) is \(\boxed{0}\).

Steps

Step 1 ：The integral is from \(\pi\) to \(\pi\), which means the lower limit and the upper limit of the integral are the same. In such cases, the value of the integral is always zero, regardless of the function being integrated. Therefore, there is no need to actually perform the integration.

Step 2 ：Final Answer: The value of the integral \(\int_{\pi}^{\pi} \sin ^{2}(x) \cos ^{4}(x) d x\) is \(\boxed{0}\).

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