Recent content by Ainlaen

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    What is the total variation of sin(x) on [a,b]?

    I was completely unaware of that. It seems to work perfectly, thank you.
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    What is the total variation of sin(x) on [a,b]?

    I'm not aware of any way to compute the variation using an integral. ##\int_a^b|\sin(x)|dx## gives the correct answers for multiples of ##\frac{\pi}{2}## but not for say ##\frac{3\pi}{4}## to ##\frac{5\pi}{4}##.
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    What is the total variation of sin(x) on [a,b]?

    ##\underset{[a,b]}{\text{Var}}(g) = \sup\{v(g,P):P\text{ is a partition of }[a,b]\}## and ##v(g,P)=\sum_{i=1}^n|g(x_i)-g(x_{i-1})|, P=\{x_0,x_1,...,x_n\}## I'm aware of no special rules for finding variation aside from when a function is monotonic. In that case...
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    What is the total variation of sin(x) on [a,b]?

    Homework Statement For a given function ##g:[a,b]→ℝ, 0 < a < b##, compute its total variation \underset{[a,b]}{\mathrm{Var}} (g) where ##g(x) = \sin(x), x\in[a,b].## Homework EquationsThe Attempt at a Solution I know that between odd multiples of ##\frac{\pi}{2}##, ##\sin(x)## is monotone, so...