- #1

quasar987

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[tex]\lim_{\delta_{\sigma}\rightarrow 0}\sum_{k=0}^{N-1}\frac{|c(t_k+\Delta t_k)-c(t_k)|}{\Delta t_k}\Delta t_k=\int_a^b |\frac{dc}{dt}(t)|dt[/tex]

Proving this would also amount to proving

[tex]\lim_{\delta_{\sigma}\rightarrow 0}\sum_{k=0}^{N-1}\frac{|c(t_k+\Delta t_k)-c(t_k)|}{\Delta t_k}\Delta t_k=\lim_{\delta_{\sigma}\rightarrow 0}\sum_{k=0}^{N-1} |\frac{dc}{dt}(t_k)|\Delta t_k[/tex]

Is there a way to do this using a finite succession of arguments?