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- Jan 26, 2012

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Many thanks to TheBigBadBen for this week's problem!

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**Problem**: Suppose that \(\displaystyle E\subset [0,2\pi]\) is a measurable set and that \(\displaystyle \int_E x^n \cos(x) \,dx=0\) for all integers \(\displaystyle n\geq 0\). Show that \(\displaystyle m(E)=0\)

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**Hint**:

Chebychev's inequality may come in handy here.

Remember to read the POTW submission guidelines to find out how to submit your answers!