Integration using Euler's formula: Difference between revisions

Revision as of 22:20, 10 October 2016

Revision as of 13:36, 23 October 2016

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Consider the integral

:<math>\int \cos^2 x \, dx.</math>

The standard approach to this integral is to use a [[half-angle formula]] to simplify the integrand. We shallcan use Euler's identity instead:

:<math>\begin{align}

\int \cos^2 x \, dx \,&=\, \int \left(\frac{e^{ix}+e^{-ix}}{2}\right)^2 dx \\[6pt]