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Homework Help: Evaluate the definite integral

  1. Oct 12, 2006 #1
    the definite integral:

    from a = (-pi/2) to (pi/2) f(((x^2)(sinx))/(1+x^6))dx

    this is the way it seems most logic to me to set it up using substitution:

    u = x
    du = dx

    from a = (-pi/2) to (pi/2) f(((u^2)(sinu))/(1+u^6))du

    = (((-cos(u))(1/3u^3))/(u+1/7u^7))+C

    I know how to evaluate it from here, I just need some feedback on my substitution setup.

    Thanks in advance.
  2. jcsd
  3. Oct 12, 2006 #2
    That sort of substitution does nothing but change the letter denoting the variable.
  4. Oct 12, 2006 #3


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    Try sketching the graph. Notice anything?

    I'm worried about what "Take the square root of the numerator and denominator" could possibly mean? I don't see how your substitution gives what you claim it gives either.
  5. Oct 12, 2006 #4
    yeah, I made a mistake. I took the integral of the square root of the function instead of the actual function.
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