Lesson 9 - Trigonometric Substitution

I. Study Section 7.3. Read with pencil and paper in hand, taking notes.

General principle: Any time you have a sum or difference of squares, or , particularly under a square root sign, then this is a possible case for integration by trigonometric substitution.

Example 1.

		dx =
	x2

Tip. Use the triangle at the right to assist in using trig substitution. Click on the link above to see a solution. Explain why there is a minus sign in the square root. Is this really a use of the Pythagorean Theorem?

Example 2.

		dx =
	x2

Example 3.

	x3
		dx =

Drill Problems using Trigonometric Substitution form Visual Calculus.