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Integrate the function (x-4)/(x^2+4) from 0 to 2

  1. Sep 23, 2008 #1
    I'm stuck on a calculus problem.

    The intagral (from 0 to 2) of (x-4)/(x^2+4)

    I figure you can split it as

    x/(x^2+4) - 4/(x^2+4)

    but I have no idea what to do after.
     
  2. jcsd
  3. Sep 23, 2008 #2
    Re: Integral

    that looks like the right step. I would suggest two different strategies for each term in the integral then. The first one looks like a u-substitution. The second looks like one of those gross inverse trig function anti-derivatives, see if you can look them up.
     
  4. Sep 23, 2008 #3
    Re: Integral

    humm...I get

    1/2ln(x^2 + 4) - 2arctan(x/2)

    can someone double check for me? I'm pretty sure its right
     
  5. Sep 23, 2008 #4
    Re: Integral

    looks good to me
     
  6. Sep 23, 2008 #5
    Re: Integral


    I think it should be 1/2 ln(x^2 + 4) - arctan(x/2). Take a look at the second integral; when you factor out the 4 in the denominator it will cancel with the 4 in the numerator so it should not be -2arctan(x/2) but just -arctan(x/2).

    Also don't forget your limits of integration
     
  7. Sep 24, 2008 #6

    Dick

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    Science Advisor
    Homework Helper

    Re: Integral

    No, it's -2*arctan(x/2). grouchy's answer is correct. What's your problem? I think you are forgetting the dx part. Differentiate the given answer to check.
     
  8. Sep 24, 2008 #7
    Re: Integral

    Ah. Oops. Your right.
     
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