# Very Simple Question, please help: Integral of a derivative squared

by gilgtc
Tags: derivative, integral, simple, squared
 P: 6 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!
 P: 659 I think partial integration can work.
 P: 70 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?
P: 659

## Very Simple Question, please help: Integral of a derivative squared

Wait a second is x(t) explicitly known?
 P: 6 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!
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,708 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$$ even has an elementary anti-derivative.
 P: 659 I dont think you can just integrate $$\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$$
 P: 6 I thought that there was an easy equivalence like: $$\int(dx/dt)dt = x$$ I guess not! thanks for your help in any case.

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