How to prove that ∫π0log(|sint|)dtis integrable
Any hints would be appreciated.
Answer
Hint: It is true that sint≥2πt on the interval [0,π/2]; try drawing the graph, or noting that sint is concave down and we have equality at the endpoints. Now show that
∫π/20|ln2πt|dt<∞
Do something similar for the right-half of the interval.
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