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Calculus 2: Trigonometric Substitution, using Z = tan(x/2)

  1. Oct 18, 2009 #1

    kiz

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

    2e2jsc8.jpg

    2. Relevant equations

    25rlguf.jpg


    3. The attempt at a solution

    After substituting:

    2cf7axc.jpg

    Using
    14wzxiw.jpg
    2yo47qx.jpg

    I'm stuck here:
    dzlsp.jpg

    I can't seem to find anything online about this substitution. Any help would be appreciated. thanks.
     
  2. jcsd
  3. Oct 18, 2009 #2
    I am so glad I have no need to remember any of this. my computer does all the calculations for me :)
     
  4. Oct 18, 2009 #3

    Dick

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    Science Advisor
    Homework Helper

    http://en.wikipedia.org/wiki/Tangent_half-angle_formula You seem to have turned a '2' into a 'z' in you dx derivation. And you would have to change the limits to 'z' limits instead of 'x' limits if you are going to stick with the variable z. Otherwise just find the indefinite integral in terms of z and change the function back to x.
     
  5. Oct 18, 2009 #4

    kiz

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    Okay, thanks for the help, I'm looking at the solution and it has [tex]1[/tex] and [tex]\sqrt{3}[/tex] for the bounds, but I do not get that when insert [tex]\frac{\pi}{3}[/tex] and [tex]\frac{\pi}{2}[/tex].

    EDIT:

    I got it, guess im blind. Thanks again.
     
    Last edited: Oct 18, 2009
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