Integration of even powers of sine and cosine

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SUMMARY

The discussion focuses on the integration of even powers of sine and cosine, specifically utilizing the double angle formulas and the Pythagorean identity. The participant initially considers the tedious nature of applying the double angle formulas repeatedly but ultimately discovers a more efficient approach using the identity cos²x + sin²x = 1. This realization simplifies the integration process significantly.

PREREQUISITES
  • Understanding of trigonometric identities, specifically cos²x + sin²x = 1
  • Familiarity with double angle formulas for sine and cosine
  • Basic knowledge of integration techniques in calculus
  • Experience with solving trigonometric integrals
NEXT STEPS
  • Study the application of double angle formulas in integration
  • Learn advanced techniques for integrating trigonometric functions
  • Explore the use of Pythagorean identities in calculus problems
  • Practice solving integrals involving even powers of sine and cosine
USEFUL FOR

Students studying calculus, particularly those focusing on trigonometric integrals, as well as educators seeking efficient methods for teaching integration techniques.

lydia_y620
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Homework Statement


upload_2017-11-7_14-14-38.png


Homework Equations


cos2x = (1+cos2x)/2
sin2x = (1-cos2x)/2

The Attempt at a Solution


I believe you would use the double angle formula repeatedly but that is very tedious; is there a more concise way to solve the problem?
 

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What about using ##cos^2x + sin^2x =1##?
 
PeroK said:
What about using ##cos^2x + sin^2x =1##?
okay, I've figured it out. Thanks!
 
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