Integration by parts difficulties

[falcao]

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:


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

to

$$m\left[\dot{y}_{\scriptscriptstyle A} \eta\right]_{t_{1}}^{t_{2}} - m\int_{t_{1}}^{t_{2}}\left(\ddot{y}_{\scriptscriptstyle A} + g\right)\eta\,dt$$ (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 $$\eta$$ 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!
$$\int u\,dv = uv - \int v\,du$$
Thanks in advance! (ps. I can post further workings if necessary)

 

[Mute]

He only did integration by parts on the first term in the integral, the $\dot{y}_A\dot{\eta}$ term. The $g\eta$ term was not integrated by parts. $u = \dot{y}_A$, $dv = \dot{\eta}dt$.

 

[falcao]

He only did integration by parts on the first term in the integral, the $\dot{y}_A\dot{\eta}$ term. The $g\eta$ term was not integrated by parts. $u = \dot{y}_A$, $dv = \dot{\eta}dt$.

sorry, my bad, although I probably wouldn't have realized if I looked at it for a full day! thanks for your help