Mathematical Methods in the Physical Sciences · Problem 11.21

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · contour-integration-verify-formula

Problem

Verify the formula by contour integration or as indicated. Assume a>0a > 0, m>0m > 0. ∫02πdθa+bsin⁡θ=∫02πdθa+bcos⁡θ=2πa2−b2,∣b∣<a\int_0^{2\pi} \frac{d\theta}{a+b\sin\theta} = \int_0^{2\pi} \frac{d\theta}{a+b\cos\theta} = \frac{2\pi}{\sqrt{a^2-b^2}}, \qquad |b| < a

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