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S = contains supplemental resources
Course: Calculus II
Topic: Integration Techniques
Subtopic: Trigonometric Integrals

Overview

Our focus today is on evaluating integrals of products or quotients of trigonometric functions such as ∫sin3x cos2x dx and ∫sec5x dx, or ∫sin5x/cos3x dx. These trigonometric integrals may require rewriting via identities, u-substitutions, and/or integration by parts. Each type of integral requires a particular plan of attack which we study in this lesson.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 8.2.1 Evaluate integrals of the form ∫sinmx cosnx dx when (1) m is odd, (2) n is odd, or (3) m and n are even.
• 8.2.2 Evaluate integrals of the form ∫tanmx secnx dx when (1) m is odd, (2) n is even, (3) m even with n odd, (4) m=0, or (5) n=0.
• 8.2.3 Using product-to-sum trigonometric identities to evaluate integrals of the form ∫sin(ax)cos(bx)dx.

Terminology

Define: products of trig functions, quotients of trig functions, trig function of a sum or difference

Supplemental Resources (optional)