Integral over many periods of a periodic trigonometric function

This type of question, asked 2 times: 26 Jul 2022, 2 Apr 2026 S2. All 2 questions below, oldest first.

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Question 1
26 Jul 2022
159 $\ \int_{0}^{20\pi} (|\sin x| + |\cos x|)^{2}dx$
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Question 2
2 Apr 2026 S2
67 $\int_{0}^{20\pi} \left( \sin^{4}x +\cos^{4}x \right)dx$
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