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Homework Help: Integration Problem

  1. Sep 20, 2008 #1
    [SOLVED]Integration Problem

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

    [tex]\int \sqrt{(6t)^2 + (10t)^2} = \int \sqrt{36t^2 100t^2} = \int \sqrt{136t^2} = \sqrt{136} \int \sqrt{t^2} = \sqrt{136} \int t[/tex]

    2. Relevant equations



    3. The attempt at a solution
    Have I made a mistake anywhere? because its from -1 to 2, so I keep getting [tex]1.5\sqrt{136}[/tex] but it says it's wrong. Any ideas?
     
    Last edited: Sep 21, 2008
  2. jcsd
  3. Sep 20, 2008 #2

    Dick

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    Homework Helper

    This a lot like integrating sqrt(t^2) from -1 to 1. If you simplify that to t, integrate to t^2/2 and put in the limits, you get 0. That's wrong. sqrt(t^2)=|t| NOT t. It's best to do the positive and negative ranges separately.
     
  4. Sep 20, 2008 #3
    So something like this:

    [tex]\sqrt{136} ( \int t \ dt + \int -t \ dt)[/tex]

    where the first integral is from -1 to 1 and the second one is 1 to 2?
     
  5. Sep 20, 2008 #4
    -1 to 0 and from 0 to 2, since |t|=t, if t>0, and |t|=-t, if t<0
     
  6. Sep 21, 2008 #5
    Got it, thank you.
     
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