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Calculators An integral my Ti-89 refused to do

  1. Sep 26, 2007 #1
    1. The problem statement, all variables and given/known data

    Indefinite integral of sin(x)/(1+x^2)dx


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 26, 2007 #2

    HallsofIvy

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    What reason do you have to believe that has an indefinite integral that can be written in terms of elementary functions?
     
  4. Sep 26, 2007 #3
    i m sorry i dont really comprehend what you are trying to say here.

    By the way my mistake on my behalf, it is the integral between the interval of -1 and 1

    I dont know how to get started
     
  5. Sep 26, 2007 #4

    Avodyne

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    This question has a very simple answer. Try graphing the function from -1 to 1 and you might see it.
     
  6. Sep 26, 2007 #5
    i realized that in the first place, but is there a mathematical manipulation that could get the result?
     
  7. Sep 26, 2007 #6

    Avodyne

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    Break the integral up into integrals from -1 to 0 and from 0 to 1. In the first, make a change of variable, x -> -x.
     
  8. Sep 26, 2007 #7
    i dont understand what you are saying >.<

    i started calc this year.

    Could you show me your steps really quick
     
  9. Sep 26, 2007 #8

    Avodyne

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    First tell me what the value of the integral is, and give your best explanation.
     
  10. Sep 26, 2007 #9
    according to the graph it's 0 because the line is reflected on the origin so the two regions canceled each other out.
     
  11. Sep 26, 2007 #10

    Avodyne

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    Yes, exactly. So the integral over the left half (from -1 to 0) must equal minus the integral over the right half (from 0 to 1).

    Do you know how to change variables in an integral? You want to change the variable in the left-half integral from x to -x, and then show that the result is equal to minus the right-half integral.
     
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