Is the Given Function an Even Function?

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Homework Help Overview

The discussion revolves around determining whether a given function is an even function, with participants exploring properties and substitutions related to the function.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relevance of the function being even, particularly in relation to symmetric limits of integration. There are inquiries about various substitutions attempted and their outcomes.

Discussion Status

Participants are actively engaging with each other's suggestions regarding substitutions and properties of even functions. Some guidance has been offered, and there is a recognition of the importance of the limits of integration in the context of the problem.

Contextual Notes

There is mention of specific properties and substitutions that may be relevant, but the exact details of these are not fully explored. The discussion reflects a collaborative effort to clarify the problem without reaching a definitive conclusion.

zorro
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Homework Statement


gif.latex?\textup{Evaluate}&space;\&space;\int_{\frac{1}{2}}^{2}\frac{sin(x-\frac{1}{x})}{x}dx.gif



The given function is an even function. I tried using properties but did not get any satisfying result.
 
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Have you tried a substitution?
 
The fact that the function is even is relevant only when the limits of integration are symmetric, with a = -b.
 
LeonhardEuler said:
Have you tried a substitution?

I tried many things :biggrin:
But did not get any solution.

Mark44 said:
The fact that the function is even is relevant only when the limits of integration are symmetric, with a = -b.

Yes I forgot about that. Which property shall I use then?
 
What substitutions did you try? If you look carefully at what you get from the substitution, the answer might pop out even though it looks like you've reached a dead end.
 
LeonhardEuler said:
What substitutions did you try? If you look carefully at what you get from the substitution, the answer might pop out even though it looks like you've reached a dead end.

I looked carefully. Nothing popped out.
Now can you tell me what is that substitution?
 
Try u=1/x
 
heck that is easy!
Thanks! I got it as 0.
 

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