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I have trouble solving this integral

$$\int_{-1}^1 \int_0^{π} \sin(x)e^{\cos y} \,dy\,dx$$

Any advice on this would be really helpful.

hwood87
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aa23
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    Formatting tip: your posts will look nicer and be easier to read if you use \sin, \cos and so on for standard functions. – saulspatz Sep 03 '21 at 20:23
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    Hint: It splits into a product of two separate integrals for $x$ and $y$. One of these is so easy that you don't even need to do the other (quite hard) one. – Troposphere Sep 03 '21 at 20:36

1 Answers1

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I think you are just having trouble with the first integral

$$\int_0^{\pi}e^{\cos(y)}dy$$

See question :What is the integral of $e^{\cos x}$

But quite simply, since the outer integral is $\int_{-1}^1\sin(x)dx$ which is an odd function therefore the integral is $0$

hwood87
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