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[tex] \int_{t_o}^{t_f}\frac{t}{\gamma} [/tex] Of course, [tex] \gamma [/tex] has no dependence on t because v is constant, so we get: [tex] \int_{t_o}^{t_f}\frac{t}{\gamma} = \frac{t_f-t_o}{\gamma} [/tex]

My question is if this can be plainly extended to accelerated reference frames where the velocity is changing. In other words is this equation valid for calculating elapsed time when velocity varies : [tex] \int_{t_o}^{t_f}\frac{t}{\gamma(t)} [/tex] where [tex] \gamma(t) [/tex] is the lorentz factor at time t?

I will try to make this more clear later. Any insight is appreciated.