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Integration by parts difficulties

  1. Aug 23, 2010 #1
    Just working through a problem Acheson's book (From Calculus to Chaos) if anyone knows it.. eq 8.6 in this book..

    As he's working through the problem he makes the step of this:


    [tex]
    m\int_{t_{1} }^{t_{2}} \left( \dot{y}_{\scriptscriptstyle A }\dot{\eta} - g\eta \right)\,dt
    [/tex] (1)

    to

    [tex]m\left[\dot{y}_{\scriptscriptstyle A} \eta\right]_{t_{1}}^{t_{2}} -
    m\int_{t_{1}}^{t_{2}}\left(\ddot{y}_{\scriptscriptstyle A} + g\right)\eta\,dt
    [/tex] (2)

    ... using integration by parts.

    Now, I've been stuck on it for a little while and I can't really figure it out.. I tried 'taking out' the [tex]\eta[/tex] but had no luck, if anyone had any suggestions of what to let == dv and what to let == u in the formula it would probably sort me out!
    [tex]\int u\,dv = uv - \int v\,du
    [/tex]
    Thanks in advance! (ps. I can post further workings if necessary)
     
  2. jcsd
  3. Aug 23, 2010 #2

    Mute

    User Avatar
    Homework Helper

    He only did integration by parts on the first term in the integral, the [itex]\dot{y}_A\dot{\eta}[/itex] term. The [itex]g\eta[/itex] term was not integrated by parts. [itex]u = \dot{y}_A[/itex], [itex]dv = \dot{\eta}dt[/itex].
     
  4. Aug 23, 2010 #3

    sorry, my bad, although I probably wouldn't have realised if I looked at it for a full day! :redface:


    thanks for your help
     
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