Uploaded July 2017 | Updated September 2026, 2 weeks ago
In this video, I show how to evaluate definite integrals involving sines and cosines by taking advantage of the polar representation of complex numbers and then applying the Residue Theorem. I look at one simple example and one complicated example of an integration which takes advantage of the Residue Theorem.
In many ways, the Residue Theorem makes life a lot more simple by allowing the evaluation of integrals that would otherwise be difficult to compute using the techniques you learned from Calculus 2. I also hope that this video satisfies some of the requests I've been getting on this topic.
Prereqs: Everything before this video in this playlist: youtube.com/playlist?list=PLdgVBOaXkb9CNMqbsL9GTWwU542DiRrPB
Questions/requests? Let me know in the comments!
Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4d2dTVjE1S2ktZnM/view?usp=sharing&resourcekey=0-eThRXWa16I1MWHeVJZgQUA
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
In this video, I show how to evaluate definite integrals involving sines and cosines by taking advantage of the polar representation of complex numbers and then applying the Residue Theorem. I look at one simple example and one complicated example of an integration which takes advantage of the Residue Theorem.
In many ways, the Residue Theorem makes life a lot more simple by allowing the evaluation of integrals that would otherwise be difficult to compute using the techniques you learned from Calculus 2. I also hope that this video satisfies some of the requests I've been getting on this topic.
Prereqs: Everything before this video in this playlist: youtube.com/playlist?list=PLdgVBOaXkb9CNMqbsL9GTWwU542DiRrPB
Questions/requests? Let me know in the comments!
Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4d2dTVjE1S2ktZnM/view?usp=sharing&resourcekey=0-eThRXWa16I1MWHeVJZgQUA
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
