Single Variable Calculus

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

Clip 1: Review of Trigonometric Identities

Clip 2: Integral of sinn(x) cos(x)

Clip 3: Integral of sin3(x) cos2(x)

Clip 4: Integral of sin3(x)

Recitation Video

Trig Integral Practice

Trig Integrals and a Volume of Revolution

Worked Example

Integral of cos³(2x)

• Problem (PDF)
• Solution (PDF)

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