Integration by parts (2-x)cos(nPi/2)x?

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SUMMARY

The discussion focuses on integrating the function (2-x)cos(nPi/2)x over the interval (1,2) using integration by parts. The user, Splint, initially struggles with the integration due to confusion regarding the constant nPi/2. However, it is clarified that nPi/2 is treated as a constant during integration. The function is defined as f(x) = (1 for 0 PREREQUISITES

  • Understanding of integration by parts
  • Familiarity with Fourier transforms
  • Knowledge of piecewise functions
  • Basic trigonometric functions and their properties
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  • Study the method of integration by parts in detail
  • Explore Fourier series and their applications
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  • Review trigonometric identities and their use in integration
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Students studying calculus, particularly those focusing on integration techniques and Fourier analysis, as well as educators seeking to clarify integration by parts and piecewise functions.

Splint
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Homework Statement


Hi,

I'm doing fouier transforms and I'm not sure how to integrate (2-x)cos(nPi/2)x, (1,2). Anyone able to help me out? Even the indefinite integral would be fine.

Homework Equations



The Attempt at a Solution


I guess u would be (2-x) and dv would be cos(nPi/2)x dx. I'm not sure how to handle (nPi/2) since it is not a constant. Does (nPi/2) stay with x at all times?

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
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n pi/2 IS a constant during the integration with respect to x.
Yes, it will be fine if you integrate by parts. How is the function exactly defined? Are you sure that you wrote the cosine function correctly? .

ehild
 
Last edited:
Thanks Ehild,

It's actually a half range expansion. The function is:

f(x)= (1, 0<x<1
(2-x, 1=<x=<2

So I believe the cosine function is correct. I won't try and integrate it right now but I should be ok with it.

Many thanks
Splint
 

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