Integration using Euler's formula: Difference between revisions

Revision as of 11:20, 12 January 2025

Revision as of 19:47, 12 January 2025

Line 2:

{{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's Formula to Integrate|journal=American Review of Mathematics and Statistics|date=2019 |publisher=American Research Institute for Policy Development|volume=7|pages=1–2|doi=10.15640/arms.v7n2a1|doi-broken-date=1 November 2024 |issn=2374-2348|eissn=2374-2356|doi-access=free|hdlurl=2158https:/1183208|hdl/arms.thebrpi.org/vol-access=free7-no-2-december-2019-abstract-1-arms }}</ref>

==Euler's formula==