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I'm reading in my modern physics book about relativistic kinetic energy. I'm a little confused about what rule of calculus allows the following statement:

[tex]

KE = \int_{0}^{s} \frac{d(mv)}{dt} ds = \int_{0}^{mv} v d(mv)

[/tex]

I see that they must be saying

[tex]

KE = \int_{0}^{s} \frac{d(mv)}{dt} ds = \int_{0}^{mv} \frac{ds}{dt} d(mv)

[/tex]

since

[tex]

\frac{ds}{dt} = v

[/tex]

But I don't understand how you can treat the differentials that way, and how you would know how to change the limits of integration when you made that change of variables. It seems like I must just be forgetting something basic.

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# Homework Help: Kinetic Energy

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