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!
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,556 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$$ even has an elementary anti-derivative.
 P: 682 I dont think you can just integrate $$\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.