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Calc 2 Integration with trig

  1. May 3, 2013 #1
    This isn't homework, It is just book problems that I am practicing, I am checking some answers with wolfram and others with the book answers.

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

    [tex]
    \begin{align}
    \int \frac{sin(w)\,dw}{\sqrt{1-cos(w)}}\\
    \end{align}
    [/tex]


    2. Relevant equations

    I used u substitution... Not sure if I approached this problem the correct way

    3. The attempt at a solution

    [tex]
    \begin{align}
    \int \frac{sin(w)\,dw}{\sqrt{1-cos(w)}}\\
    \end{align}
    [/tex]

    Using U sub... U = cos(w), du = -sin(w)

    [tex]
    \begin{align}
    - \int \frac{\,du}{\sqrt{1-u}}\\
    \end{align}
    [/tex]

    Using n sub... n=1-u, dn = -1

    [tex]
    \begin{align}
    \int \frac{\,du}{\sqrt{n}} = 2\sqrt{(1-cos(w))} + C\\
    \end{align}
    [/tex]
     
    Last edited: May 3, 2013
  2. jcsd
  3. May 3, 2013 #2

    Mark44

    Staff: Mentor

    Looks good. One nice thing about these types of problems is that you can check them yourself. If your answer is correct, you should be able to differentiate it and get the integrand.

    As for your substitution, what you did is OK, but you can kill two birds with one stone by letting u = 1 - cos(w). Then du = sin(w)dw.
     
  4. May 3, 2013 #3
    Thank you.. I was checking the integrals on wolfram but it seems to work much better if I take my answer and try to get the integral. And I can't believe I didn't think of the 1-cos(w) substitution :redface:

    I just found this forum and you guys have been a lot of help! Maybe one day i will be good enough to answer other people's questions.
     
  5. May 3, 2013 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Speaking of using WolframAlpha, their result for this integration is ##\displaystyle \ \frac{4 \sin^2(x/2)}{(1-\cos(x))^{3/2}}+C \ .##

    By the way, this is equivalent to your answer.
     
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