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Non elementary integral

  1. Jul 14, 2011 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=37197&stc=1&d=1310695247.jpg


    2. Relevant equations



    3. The attempt at a solution

    Well, I just want some hint.
    It seems substitution doesn't work.(I can't think of any suitable substitution)
     

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  3. Jul 14, 2011 #2
    These all seem to be like special functions, like for the first one, http://press.princeton.edu/books/maor/chapter_10.pdf [Broken] however, you probably know that :x!
     
    Last edited by a moderator: May 5, 2017
  4. Jul 14, 2011 #3

    SammyS

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    Try changing the order of integration. Is that one of the subjects that is covered in the section of the textbook in which you found these problems?
     
  5. Jul 14, 2011 #4
    This chapter is about Multiple integrals, but it doesn't cover these special functions(Maybe the textbook assume we know these already).

    It seems after changing the order, nothing change.
    Take the first one as an example.
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  6. Jul 15, 2011 #5

    SammyS

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    Looking at problem 29. as it is given: [itex]\displaystyle \int_{y=0}^{\pi} \int_{x=y}^{\pi}\,\frac{\sin\,x}{x}\,dx\,dy\,,[/itex] what is the region over which the integration is to be done?

    For any given y, x goes from the line x = y (the same as y = x) to the vertical line y = π. y goes from 0 (the x-axis) to π.

    Therefore, this is the region in the xy-plane bounded by the x-axis, the line x = π and the line y = x.

    That's not the same region you integrated over after you changed the order of integration. You integrated over the region bounded by the y-axis, the line y = π and the line y = x.

    For the correct region, switching the order of integration will eliminate having to integrate "special functions".
     
  7. Jul 15, 2011 #6

    D H

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    Do this right, athrun200, and this same technique will apply to all four of those problems.
     
  8. Jul 15, 2011 #7

    SammyS

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    This may help for #29. attachment.php?attachmentid=37206&stc=1&d=1310742149.gif
     

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  9. Jul 16, 2011 #8
    While I'm not the OP, I have to say thanks as that is a cool technique that I did not know of! Thanks!
     
  10. Jul 16, 2011 #9

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  11. Jul 16, 2011 #10

    D H

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    Excellent. You got all three.
     
  12. Jul 16, 2011 #11
    I am so happy that I understand this section now:biggrin:
     
  13. Jul 18, 2011 #12

    SammyS

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    athrun200 & romsofia,

    Glad that you now understand this.


    D H,
    Thanks for checking in on these problems! I'm traveling & have been away from computer access for a few days.
     
  14. Jul 18, 2011 #13
    Last edited by a moderator: Apr 26, 2017
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