Chapter 5.3
Trigonometric substitution
What You'll Learn
Apply the Pythagorean theorem to construct right triangles for trigonometric substitution
Convert radical expressions involving sums and differences of squares into trigonometric functions
Substitute x with trigonometric expressions using sine, tangent, and secant relationships
Evaluate integrals by transforming them from algebraic to trigonometric form
Convert final answers from trigonometric functions back to expressions in terms of x
What You'll Practice
1
Integrating expressions with square roots of differences of squares using sine substitution
2
Solving integrals with square roots of sums of squares using tangent and secant substitution
3
Drawing and applying right triangle relationships to perform substitutions
4
Simplifying trigonometric expressions and applying u-substitution within trig integrals
Why This Matters
Trigonometric substitution is essential for solving complex integrals in calculus that can't be handled by basic techniques. You'll use this method throughout advanced calculus, differential equations, and physics to evaluate integrals involving radicals and rational functions.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Practice exercises
Learning resources
Skills
Trigonometric Substitution
Integration Techniques
Pythagorean Theorem
Right Triangles
Sine and Cosine
Tangent and Secant
U-Substitution
Calculus
