Integrate - Solve \int3^x\cos x\,dx w/ Partial Integration

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SUMMARY

The discussion focuses on solving the integral \(\int_3^x \cos x \, dx\) using the method of integration by parts, also known as partial integration. Participants emphasize the importance of selecting the correct function for \(u\) in the integration process. The conversation highlights the trial-and-error nature of determining the best choices for \(u\) and \(dv\) to simplify the integration.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with the method of integration by parts
  • Knowledge of the fundamental theorem of calculus
  • Basic trigonometric functions and their integrals
NEXT STEPS
  • Study the integration by parts formula: \(\int u \, dv = uv - \int v \, du\)
  • Practice solving integrals involving trigonometric functions
  • Explore examples of choosing \(u\) and \(dv\) effectively
  • Learn about definite integrals and their applications
USEFUL FOR

Students studying calculus, educators teaching integration techniques, and anyone looking to improve their skills in solving integrals using partial integration.

Government$
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Homework Statement



Integrate [itex]\int3^x\cos x\,dx[/itex]

The Attempt at a Solution



It has to be done using partial integration.

I don't know what should be u?
 
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What choices do you have?
 
You're just going to have to try stuff out and see how it works out.
 

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