Compute causal function using integration by parts

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SUMMARY

The discussion focuses on the application of the integration by parts method to compute a causal function, specifically addressing the integral ∫ T.sin3(t-T).dT. The user seeks clarification on the transition from this integral to the subsequent steps in the solution. The correct evaluation of this integral is confirmed as essential for progressing in the problem, highlighting the importance of understanding convolution details in this context.

PREREQUISITES
  • Integration by parts methodology
  • Understanding of causal functions
  • Basic knowledge of convolution in mathematics
  • Familiarity with trigonometric integrals
NEXT STEPS
  • Study the integration by parts technique in detail
  • Explore convolution properties and their applications
  • Practice solving trigonometric integrals involving sine functions
  • Review examples of causal functions in mathematical analysis
USEFUL FOR

Students and educators in mathematics, particularly those studying calculus and integral techniques, as well as anyone looking to deepen their understanding of causal functions and convolution.

majdi
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Homework Statement


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I stuck on, when the question as for integration by parts method. Need advice
 
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Hi majdi. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

The line with ∫ T.sin3(t-T).dT is where you need to perform integration by parts, in order to get the next line.

How did you go from that line to the next? (BTW, that is the right answer after you evaluate that integral).

NB: I have forgotten convolution details, so I'm making no comment on your post before the integral by parts line.
 
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