Integration using Euler's formula: Difference between revisions

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Functions containing sine or cosine can be expressed as complex exponentials using

'''Integration using complex analysis''' is a method of integrating certain functions.

[[Euler's formula]].

SupposeExample: suppose we wanted to integrate:

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

InsteadThen ofthe usingcosine [[Integrationfunction bycan parts]],be we may substitute the cosine functionexpressed forin its Euler form: <math>\cos \theta = \frac{e^{i\theta} + e^{-i\theta}}{2}</math>

: <math>\int e^x \cdot \frac{e^{ix} + e^{-ix}}{2} \, dx</math>