Integration using complex analysis

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Homework Help Overview

The discussion revolves around the integration of the function S cos^8(t) dt from 0 to 2π, with an emphasis on utilizing complex analysis techniques. Participants are exploring how to apply the binomial theorem in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the transformation of the integral using complex exponentials and the binomial theorem. There are inquiries about how to proceed after applying the theorem and concerns regarding familiarity with the theorem itself.

Discussion Status

Some participants have suggested using the binomial theorem and converting the results back to cosine form for integration. There is an acknowledgment of varying levels of understanding regarding the theorem, with some expressing uncertainty about how to continue with the problem.

Contextual Notes

One participant notes a lack of prior study of the binomial theorem, which may be impacting their ability to progress with the problem. There is also a hint of frustration regarding the complexity of the example in relation to their current coursework.

gipc
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I have to integrate S cos^8 (t) dt from 0 to 2 pi, presumably using complex analysis

I got to S [(e^(it) + e(-it))/2]^8 dt from 0 ti 2pi

How do I take it from here?

I have a hint- use binomial theorem.
 
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Use the binomial theorem on [(e^(it) + e(-it))/2]^8, then write the answers back to cosinus form and integrate.
 
gipc said:
How do I take it from here?

I have a hint- use binomial theorem.

At the risk of being snarky, have you tried using the binomial theorem? If you have not, you really should have tried it before coming here. If you have, then you should describe why you couldn't continue from there to get the answer.
 
well, the problem is i didn't study the binomial theorem (obviously with taking the complex analysis course and not the discrete math one). and this example is a little tricky to begin with :(
 

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