Question
Using Cauchy’s residue theorem, evaluate the integral
Answer :
Word Count : 325
To evaluate the integral using Cauchy's residue theorem, we first express the integral in a complex form. The given integral is: \[ I = \int_{0}^{2\pi} \frac{d\theta}{2 + \cos\theta} \] ### Step 1: Convert to a complex integral We use the substitution \( z = e^{i\theta} \), so that \( dz = i e^{i\theta} d\theta _________ _________ _______ __________ ____ _________ ________ ___.
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To evaluate the integral using Cauchy's residue theorem, we first express the integral in a complex form. The given integral is: \[ I = \int_{0}^{2\pi} \frac{d\theta}{2 + \cos\theta} \] ### Step 1: Convert to a complex integral We use the substitution \( z = e^{i\theta} \), so that \( dz = i e^{i\theta} d\theta _________ _________ _______ __________ ____ _________ ________ ___.
______ _____ ________ ______ _________ ______ _____ _____ _______ ______ ____.
_________ ______ _______ ____ _________ __________ _________ ________ __________ _________ __________ ____.
______ _________ ______ ________ ________ ______ _______ ______ ________ __________.
__________ _____ _____ _________ ______ ______ ____.
_____ ________ _____ ______ _________.
_____ _________ _______ _______ ___ _____ _______ ____ _______ _________ _______.
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