Integration of Trigonomic Functions

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SUMMARY

The discussion centers on the integration of the function ∫cos^(3)x by parts. The user, Andy, seeks clarification on rewriting cos^(3)x in a more manageable form, specifically as cos(x)(1-sin^2(x)). This transformation is based on the Pythagorean identity sin^2(x) + cos^2(x) = 1. Participants in the forum suggest that equivalent expressions for trigonometric functions can be found in mathematical tables or resources.

PREREQUISITES
  • Understanding of integral calculus, specifically integration by parts.
  • Familiarity with trigonometric identities, particularly the Pythagorean identity.
  • Knowledge of rewriting trigonometric functions for simplification.
  • Basic skills in mathematical notation and expressions.
NEXT STEPS
  • Research trigonometric identities and their applications in integration.
  • Study integration techniques, focusing on integration by parts.
  • Explore resources for trigonometric function tables and equivalent expressions.
  • Practice integrating various trigonometric functions to reinforce understanding.
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Students studying calculus, mathematics educators, and anyone looking to improve their skills in integrating trigonometric functions.

Andyb43
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I have come across the problem of ∫cos^(3)x by parts. I have no idea how to integrate this. I know that I need to change the way I write cos^(3)x and I have seen people put cosx(1-sinx).

Please could you let me know where to find these equivilent ways of writing trigonomic formula? I assume there must be a table or something?

Thanks,

Andy

PS Sorry if this isn't the clearest explanation.



Homework Equations





The Attempt at a Solution

 
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I think you mean that cos3(x) = cos(x){1-sin2(x)} .

That's because sin2(x) + cos2(x) = 1 .
 
You're probably right. This is the problem I'm having, I don't know what the equivalent expressions are.
 

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