## Main Question or Discussion Point

Hello,

I am trying to figure out how to integrate this, I know it must be simple but I am not sure how to do it.

$$\int(\frac{dx}{dt})^{2}dt$$

Thanks a lot!

I think partial integration can work.

You just need x defined in terms of t

x = x(t)

then you can differentiate with respect to t,

then you square dx/dt

then you integrate that across t from t1 to t2

right?

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Wait a second is x(t) explicitly known?

hi, thanks for your answers. x(t) is not known that is why I am not sure how to do it. Otherwise what Nick mentioned would be easily applicable.

Any other ideas? What do you mean by partial integration dirk_mec1?

Thanks!

HallsofIvy
Homework Helper
He means "integration by parts". Do you have any reason to think that there is any simple answer to this question? I can see no reason to assume that
$$\right(\frac{dx}{dt}\)^2$$
even has an elementary anti-derivative.

I dont think you can just integrate $$\int (f'(x))^2 \mbox{d}x$$, right? The integration by parts(thanks hallsofIvy ) however gives:

$$x (x'(t))^2 - \int x \cdot 2x' \cdot x''\ \mbox{d}t$$

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re

I thought that there was an easy equivalence like:

$$\int(dx/dt)dt = x$$

I guess not! thanks for your help in any case.