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Integral of a product of three functions?

  1. Aug 25, 2009 #1
    Hello there,

    I've been battling through my books and searching the web, but nothing seems to give me any ideas on how to tackle this beast bellow:

    [tex]\int_{-\pi }^{\pi } e^{-x^{2}} \sqrt{x^{4}+1} sin x dx [/tex]

    This is a reasonably desperate call for any information or literature anyone might know of. If you know of anywhere with material on this or even which techniques I should be looking into it'd be much appreciated!

    Thanks,
    D =]
     
  2. jcsd
  3. Aug 25, 2009 #2

    VietDao29

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    Big hint of the day, when encountering these type of definite integrals with the limit from -a to a, one should immediately check to see if the given function is even, or odd. :devil:

    Can you go from here? :)

    ---------------

    EDIT: Oh, and btw, this thread shouldn't belong to Introductory Physics board.. =.="
     
  4. Aug 25, 2009 #3
    Uh.. is it odd? *crosses fingers* so it's zero?

    You might have guessed I'm new here, where should this question go?
     
  5. Aug 25, 2009 #4

    rock.freak667

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    for an odd function f(-x)=-f(x) and an even function f(-x)=f(x)

    Calculus & Beyond forum
     
  6. Aug 25, 2009 #5

    VietDao29

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    Yes, it is. It's 0.

    Let f(x) be a continuous function on the interval (-a, a).

    If f(x) is odd then:

    [tex]\int_{-a} ^ a f(x) = 0[/tex]

    And if f(x) is even then:

    [tex]\int_{-a} ^ a f(x) = 2 \int_0 ^ a f(x)[/tex]

    You can use a simple u-substitution to prove both of them. Pretty easy, just give it a try if you want. :)
     
  7. Aug 26, 2009 #6
    Thank you both very much! You have saved me a lot of misguided scribbling =]
     
  8. Aug 26, 2009 #7

    ideasrule

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    By the way, there's no indefinite integral for that function:

    http://integrals.wolfram.com/index.jsp?expr=%28e^-x^2%29*sqrt%28x^4%2B1%29*sin%28x%29&random=false
     
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