Just working through a problem Acheson's book (From Calculus to Chaos) if anyone knows it.. eq 8.6 in this book..(adsbygoogle = window.adsbygoogle || []).push({});

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)

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# Integration by parts difficulties

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