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Math Help - Definite integration proof

  1. #1
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    Definite integration proof

    Prove that \int_0^{2\pi}e^{\cos\theta}\cos(\sin\theta)=2\pi
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  2. #2
    Math Engineering Student
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    Differentiate under the integral sign, it'll be helpful to get what you want.

    Define f(\varphi ) = \int_0^{2\pi } {e^{\varphi \cos \theta } \cos (\varphi \sin \theta )} \,d\theta.

    From there, you just need to find f(1), and it's done.

    (You forgot the d\theta.)
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