Use Cauchy Integral Formula to evaluate the integral

  • Thread starter DanniHuang
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  • #1
DanniHuang
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Homework Statement



The question is needed to be done by using an appropriate substitution and the Cauchy Integral Formula.

Homework Equations



Evaluate the complex integral: ∫e^(e^it) dt, from 0 to 2∏

The Attempt at a Solution


I cannot find an appropriate substitution for the integral.
 

Answers and Replies

  • #2
Kreizhn
743
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Perhaps the best way to see how to do this question is that we somehow need to make this into a contour integral. The easiest things around which to integrate are circles right? For example, if f(z) is a complex function and we want to integrate around the unit circle [itex] \{ z \in \mathbb C: |z|^2 = 1 \} [/itex], it may be convenient to parameterize the circe as [itex] z = e^{it} [/itex]. Thus if somebody asks you to integrate [itex] e^{e^{it}} [/itex] for [itex] t \in [0,2\pi) [/itex], what function is being integrated about what contour?
 

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