Transformation by Trigonometric Identities Evaluate: integral of sin^12 2x cos^7 2x dx. Use the guide below. Fulll solution.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
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TOPIC: Transformation by Trigonometric Identities Evaluate: integral of sin^12 2x cos^7 2x dx. Use the guide below. Fulll solution.
Integrals Involving Powers of Trigonometric Functions
Ty
sin" x cos" x dx
Case 1: m or n Is an Odd Positive Integer
If m is odd, u = cos x
du = – sinx dx
sin? x =1 – cos? x
if n is odd u = sin x
du = cosx dx
cos? x = 1 – sin² x
Case 2: m and n Are Both Even Positive Integers
sin? a = (1 – cos 2a)
cos a = 5(1 + cos 2a)
Transcribed Image Text:Integrals Involving Powers of Trigonometric Functions Ty sin" x cos" x dx Case 1: m or n Is an Odd Positive Integer If m is odd, u = cos x du = – sinx dx sin? x =1 – cos? x if n is odd u = sin x du = cosx dx cos? x = 1 – sin² x Case 2: m and n Are Both Even Positive Integers sin? a = (1 – cos 2a) cos a = 5(1 + cos 2a)
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