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Session 68: Integral of sin^n(x) cos^m(x), Odd Exponents

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Overview

Finding antiderivatives of trigonometric functions can be tricky. In this session, guest lecturer Haynes Miller reviews some trigonometric identities and uses them to get antiderivatives for some products of sine and cosine.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Review of Trigonometric Identities (5 min)
» Accompanying Notes (PDF)

From Lecture 27 of 18.01 Single Variable Calculus, Fall 2006


» Clip 2: Integral of sinn(x) cos(x) (6 min)
» Accompanying Notes (PDF)

From Lecture 27 of 18.01 Single Variable Calculus, Fall 2006


» Clip 3: Integral of sin3(x) cos2(x) (5 min)
» Accompanying Notes (PDF)

From Lecture 27 of 18.01 Single Variable Calculus, Fall 2006


» Clip 4: Integral of sin3(x) (2 min)
» Accompanying Notes (PDF)

From Lecture 27 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

» iTunes U
» Internet Archive

Recitation Video

 

Trig Integral Practice

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Download this video:
» iTunes U (MP4 - 25MB)
» Internet Archive (MP4 - 25MB)

Trig Integrals and a Volume of Revolution

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Download this video:
» iTunes U (MP4 - 21MB)
» Internet Archive (MP4 - 21MB)

Worked Example

 

Integral of cos3(2x)

 

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