Let C be the unit circle z ei theta pi lessthanorequalto th

Let C be the unit circle z = e^i theta (-pi lessthanorequalto theta lessthanorequalto pi). First show that for any real constant a, integral_C e^az/z dz = 2 pi i. Then write this integral in terms of theta to drive the integration formula integral_0^pi e^a cos theta cos(a sin theta) d theta = pi.

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