- #1

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[tex]K=\int_{x_1}^{x_2}F\,dx = \int_{0}^{v}\frac{d}{dt}(mv)\,dx = \int_{0}^{v}(mv\,dv+v^2\,dm)[/tex]

here, my lecturer told us without showing that

[tex]mv\,dv+v^2\,dm = c^2\,dm[/tex]

Can someone please give me hints on how to combine these two integrals? I have no idea how to start.