Friday, 22 December 2017

calculus - How to prove that intpi0log(|sint|),textrmdt;;textrmisintegrable




How to prove that π0log(|sint|)dtis integrable 



Any hints would be appreciated.


Answer



Hint: It is true that sint2πt 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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