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I am trying to show that $$\int_{-\pi}^{\pi}e^{\alpha \cos t}\sin(\alpha \sin t)dt=0$$

Where $\alpha$ is a real constant.


I found the problem while studying a particular question in this room,this one. It becomes so challenging to me as I am trying to make life easy but I stucked!

EDIT: The integral is from $-\pi$ to $\pi$

EDIT 2: I am sorry for this edit, but it is a typo problem and I fix it now. In my question I have $e^\alpha \cos t$ not $e^\alpha$ only. I am very sorry.

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    When you write out function names like $\operatorname{sin}$ as words, $\TeX$ interprets them as a juxtaposition of variable names, which get italicized and don't have the right spacing. To get proper formatting for function names, you need to use the commands predefined for that purpose, e.g. `\sin`, or, for functions for which there's no predefined command, you can use `\operatorname{name}` to produce "$\operatorname{name}$".2012-04-19
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    @joriki:thanks I will fix it2012-04-19
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    In that answer the integral with sin is from $-\pi$ to $\pi$. Since $\sin(t)$ is odd, the integral is obviously 0...2012-04-19
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    You only fixed one out of the four incorrectly formatted instances of $\sin$ in the post.2012-04-19
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    @N.S. yes I see and I fix it, but I will not have peace of mind until I realize the obvious thing.2012-04-19
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    @joriki: It is done now.2012-04-19
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    Hassan, this is very frustrating. Please take more care in formatting your posts and in responding to comments. I've now twice pointed out the incorrect formatting of the sine functions; each time you've only corrected a single one of the four instances in the post, the second time even after I had pointed out that there are four and you had agreed and announced that you would fix them. The title is still just as badly formatted as it was originally. P.S.: I see that Arturo has fixed it now.2012-04-19
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    @joriki: As long as you understand what I mean I have no problem, because in maths we speak one language that is UNDERSTANDING.2012-04-19
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    Well then say that right away and I won't spend my time trying to help you with the formatting. What's the point of announcing that you'll change it and then not changing it?2012-04-19

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