8.3 Trigonometric Identities (Part 2) www.hiboox.com

Objectives Solve trigonometric integrals involving powers of secant and tangent.

(Look at guidelines at the bottom of page 500.) Evaluating Integrals Involving Secant and Tangent: (Look at guidelines at the bottom of page 500.) If power of secant is even and positive: Save one sec2 factor and convert remaining factors to tan. Use If power of tangent is odd and positive: Save one secxtanx factor and convert remaining factors to sec. If no sec factors and power of tan is even and positive: Convert tan2 factor to sec2. If of form where m is odd and positive, use integration by parts. If all else fails, convert to sin and cos.

Example 4: tan: power odd and positive (rule #2)

Example 5: tan: power odd and positive (rule #1) Save sec2x and convert sec to tan.

Example 6: No sec, tan is even and positive: rule #3 Convert to tan2 to sec2.

Example 7: Rule #5!

Homework 8.3 (page 542) #25 – 41 odd