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- Jan 26, 2012

- 995

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**Problem**: Let $f(x)$ be a continuous function.

- Show that $\displaystyle\int_0^a f(x)\,dx = \int_0^a f(a-x)\,dx$.
- Use (1) to show that \[\int_0^{\pi/2}\frac{\sin^n x}{\sin^n x+\cos^n x}\,dx = \frac{\pi}{4}\] for all positive numbers $n$.

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