How to Solve Trigonometric Integrals (Calculus 2 Lesson 13)

In this video we learn about how to solve trigonometric integrals of certain forms. This includes trig integrals that contain sin(x) and cos(x) where each is raised to a power, and integrals that contain sec(x) and tan(x) where each of those functions are raised to a power. We discuss the techniques that will be used to solve these integrals, as well as the important role that knowing trigonometric identities will play in solving the integrals as well. As such, we will also review the relevant pythagorean identities and half-angle identities you will need to use.

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This series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!

Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!


Video Chapters:
0:00 Intro to the Specific Forms of Trigonometric Integrals
1:17 Pythagorean Identities (Review)
2:57 Half-Angle Identities (Review)
4:31 Guidelines for Solving Sine & Cosine Integrals
5:32 Example - cos^3(x)*sin^2(x)
10:05 Example - sin^5(x)*cos^4(x)
16:45 Example - cos^2(x)*sin^2(x)
22:44 Guidelines for Solving Secant & Tangent Integrals
23:39 Example - tan(x)*sec^3(x)
26:32 Example - tan^3(x)*sec^4(x)
31:10 Example - tan^5(2x)*sec^2(2x)
34:30 Outro


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