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Find the integral x^3 sqrt(x^2 + x^8 + 8) cos x dx

  1. Dec 1, 2009 #1

    golb0016

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    1. The problem statement, all variables and given/known data
    Find the integral

    f(x) = x^3 sqrt(x^2 + x^8 + 8) cox(x) dx


    3. The attempt at a solution

    I need help starting. It appears to be either integration by parts and/or substituion.
     
    golb0016, Dec 1, 2009
  2. jcsd
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  3. Dec 1, 2009 #2

    Dick

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    Re: Integral

    You are going to have a tough time finding an antiderivative for that. Is it actually a definite integral?
     
    Dick, Dec 1, 2009
  4. Dec 1, 2009 #3

    golb0016

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    Re: Integral

    The problem wanted the function evaluated from -14 to 14. Does it make a difference if it is definitive or not? Is there a trick if it is definitive?
     
    golb0016, Dec 1, 2009
  5. Dec 1, 2009 #4

    Dick

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    Re: Integral

    It does in this case. For your function f(-x)=(-f(x)), it's an odd function. What happens if you integrate an odd function over a symmetric interval around the origin?
     
    Dick, Dec 1, 2009
  6. Dec 1, 2009 #5

    golb0016

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    Re: Integral

    Does the positive and negative parts cancel out if it is symmetric?
     
    golb0016, Dec 1, 2009
  7. Dec 1, 2009 #6

    Dick

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    Re: Integral

    That's the idea.
     
    Dick, Dec 1, 2009
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