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## Homework Statement

For a given function ##g:[a,b]→ℝ, 0 < a < b##, compute its total variation [itex]

\underset{[a,b]}{\mathrm{Var}}

(g)[/itex] where ##g(x) = \sin(x), x\in[a,b].##

## Homework Equations

## The Attempt at a Solution

I know that between odd multiples of ##\frac{\pi}{2}##, ##\sin(x)## is monotone, so the interval ##[a,b]## needs to be broken up accordingly. If ##a## and ##b## are both in the same monotone interval, we simply have ##\sin(b)-\sin(a)##. If they're split over a turn, it becomes ##|1-\sin(a)| + |\sin(b)-1|##. I've so far been unable to come up with a closed form way of describing that for arbitrary ##a## and ##b## stretching over an area greater than ##\pi##, though.