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« Integrals Involving Trigonometric Functions
Integration Techniques: (lesson 4 of 4)

Trigonometric Substitutions

Use trigonometric substitution to evaluate integrals involving the radicals,

Trigonometric Substitutions

Case I:

evaluate integrals

Example 1:

integral

Solution:

solution

Then,

solution

Example 2:

Trigonometric Substitutions example

Solution:

Let x = 2 sin θ, dx = 2 cosθ dθ

Trigonometric Substitutions solution

Case II:

Trigonometric Substitutions example

Example 3:

Trigonometric Substitutions solution

Solution:

solution

Then,

Trigonometric Substitutions

Case III:

Trigonometric Substitutions

Example 4:

example 4

Solution:

solution 4

Then,

solution 4