Integration using Euler's formula: Difference between revisions

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{{more citations needed|date=July 2019}}
{{calculus|expanded=integral}}
In [[integral calculus]], [[Euler's formula]] for [[complex number]]s may be used to evaluate [[integral]]s involving [[trigonometric functions]]. Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely <math>e^{ix}</math> and <math>e^{-ix}</math> and then integrated. This technique is often simpler and faster than using [[trigonometric identities]] or [[integration by parts]], and is sufficiently powerful to integrate any [[rational fraction|rational expression]] involving trigonometric functions.<ref>{{Cite journal|last=Kilburn|first=Korey|title=Applying Euler’sEuler's Formula to Integrate|url=https://doi.org/10.15640/arms.v7n2a1|journal=American Review of Mathematics and Statistics|publisher=American Research Institute for Policy Development|volume=7|pages=1–2|doi=10.15640/arms.v7n2a1|doi-broken-date=2024-07-28 |issn=2374-2348|eissn=2374-2356|doi-access=free|hdl=2158/1183208|hdl-access=free}}</ref>
 
==Euler's formula==