Trigonometric Substitutions
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Lesson Summary:
In this math lesson, we explore trigonometric substitutions and how they can be used to simplify integrals. We cover substitutions for sine, tangent, and secant, and provide examples of how to apply them to various types of integrals. By using these substitutions, we can transform complicated integrals into simpler ones that we can easily solve.
Lesson Description:
Sine, tangent, and secant substitutions.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
Questions answered by this video:
- What is trig substitution?
- What is sine substitution?
- What is the integral of the square root of 1 - x^2?
- How do you take the integral of the square root of 4 - x^2 / x?
- What is tangent substitution?
- How do you use secant substitution?
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Staff Review
This video explains how and why trigonometric substitution works. You will see the right triangle trigonometry that helps you remember how it all works. Then, some really great examples are shown depicting trig substitution. There is a really helpful summary at the end of the video that explains when to use each substitution, when you have a^2 - u^2, a^2 + u^2, or u^2 - a^2.
