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Problem on properties of D.I.

  • Thread starter zorro
  • Start date
  • #1
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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.
 

Answers and Replies

  • #2
LeonhardEuler
Gold Member
859
1
Have you tried a substitution?
 
  • #3
33,646
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The fact that the function is even is relevant only when the limits of integration are symmetric, with a = -b.
 
  • #4
1,384
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Have you tried a substitution?
I tried many things :biggrin:
But did not get any solution.

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?
 
  • #5
LeonhardEuler
Gold Member
859
1
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.
 
  • #6
1,384
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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?
 
  • #8
1,384
0
heck that is easy!
Thanks! I got it as 0.
 

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