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Post Closed as "off topic" by Douglas Zare, Willie Wong, Pietro Majer, Michael Renardy, George Lowther
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Let $g$ be Riemann integrable on $[a,b]$, $f(x)=\int_a^xg(t)dt$ for $x∈[a,b]$. How to show that the total variation of $f$ is equal to $∫_b^a|g(x)|dx$?∫_a^b|g(x)|dx$? |
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Question about Riemann integral and total variationLet $g$ be Riemann integrable on $[a,b]$, $f(x)=\int_a^xg(t)dt$ for $x∈[a,b]$. How to show that the total variation of $f$ is equal to $∫_b^a|g(x)|dx$?
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