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Please help me to solve this integration problem

  1. Mar 5, 2014 #1

    lap

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    Integrate ( (sqrt (x^2 - 9))/x )( exp x^2 )( cos 7x )( sin(x^4 + 5x^2 + 100) ) dx
    with upper limit = 3 and lower limit = -3

    I have tried to use integration by part and set u = ( (sqrt (x^2 - 9))/x )( exp x^2 ) and
    dv = ( cos 7x )( sin(x^4 + 5x^2 + 100) ) dx
     
    Last edited: Mar 5, 2014
  2. jcsd
  3. Mar 5, 2014 #2

    adjacent

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    What have you tried so far?
     
  4. Mar 5, 2014 #3

    Ray Vickson

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    I very much doubt there is any closed-form formula for the antiderivative, so you probably need to contemplate numerical integration for the general case of ##\int_a^b f(x) \, dx##. However, before doing that, sit down and think carefully about your specific problem.
     
  5. Mar 5, 2014 #4

    lap

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    How to integrate ( (sqrt (x^2 - 9))/x )( exp x^2 )( cos 7x )( sin(x^4 + 5x^2 + 100) ) dx ?
     
  6. Mar 5, 2014 #5

    Ray Vickson

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    I have already told you it cannot be done with formulas---even very long ones having billions of complicated terms and taking millions of pages to write out. However, that was not your original question: you wanted ##\int_{-3}^3 f(x) \, dx##. As I suggested, think hard about the problem first.
     
  7. Mar 6, 2014 #6

    lap

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    The answer is 0 ?
     
  8. Mar 6, 2014 #7
    The answer is correct but can you prove it?
     
  9. Mar 6, 2014 #8

    lap

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    I know the answer is 0 because the positive area canceled the negative area but I don't know how to prove it
     
  10. Mar 6, 2014 #9

    Dick

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    If f(x) is that big expression you are integrating, can you prove that f(-x)=(-f(x))? Then show ##\int_{-a}^0 f(x) dx = -\int_{0}^a f(x) dx##.
     
    Last edited: Mar 6, 2014
  11. Mar 6, 2014 #10

    lap

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    I proved that f(-x)=(-f(x)) and solved it. Thank you very much !
     
  12. Mar 6, 2014 #11

    HallsofIvy

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    In order to use symmetry here you must also show that this is not an improper integral. Your integrand is a fraction with sin(x^4+ 5x^2+ 100) in the denominator. Can you show that this never 0 for x between -3 and 3?
     
  13. Mar 6, 2014 #12
    There is an x in the denominator instead of sine. Moreover, the function doesn't seem to defined within the given limits.
     
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