Question

A special case of the Riemann–Stieltjes integral

score 27 · Answer 1 · 2026-03-26 14:34:35

27

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A special case of the Riemann–Stieltjes integral

Published on 26 Mar 2026 - 14:34

score 47 · Answer 2 · 2026-04-02 00:32:29

47

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Darboux integrability implies Riemann integrability in $\mathbb{R}^n$

Published on 02 Apr 2026 - 0:32

score 59 · Answer 3 · 2026-04-02 00:28:39

59

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Spivak's Calculus, Ch. 13 Appendix "Riemann Sums, Problem 3: Prove formula for length of parametric curve based on inscribed polygonal curve.

Published on 02 Apr 2026 - 0:28

score 55 · Answer 4 · 2022-07-04 16:31:45

55

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Potential problem with a proof involving Riemann Integral

Published on 04 Jul 2022 - 16:31

score 63 · Answer 5 · 2026-04-02 00:28:39

63

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What happens if you relax the "for all" requirement of Darboux integration?

Published on 02 Apr 2026 - 0:28

score 254 · Answer 6 · 2022-07-06 17:51:52

254

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For any $f\in C^1[0,1]$ show that $\sum_{k=1}^n f\big(\frac{k}{n}\big) - n \int_0^1 f(x)dx$ converges to $\frac{f(1)-f(0)}{2}$ as $n \to \infty$.

Published on 06 Jul 2022 - 17:51

score 89 · Answer 7 · 2022-07-07 01:53:43

89

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Prove or disprove: If $\int_0^1f(t)t^{2n+1}dt=0$ for each integer $n\geq 0$, then $f=0$ on $[0 ,1]$.

Published on 07 Jul 2022 - 1:53

score 57 · Answer 8 · 2022-07-08 11:33:16

57

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When is the indicator of a sublevel set integrable?

Published on 08 Jul 2022 - 11:33

score 117 · Answer 9 · 2026-04-02 00:24:36

117

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Problem in Riemann Summation method

Published on 02 Apr 2026 - 0:24

score 157 · Answer 10 · 2022-07-10 09:05:57

157

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Is there a function $f:[0,\infty) \to \{-1, 1\}$ such that $\int_0^\infty{f(x)\,dx}$ is well defined?

Published on 10 Jul 2022 - 9:05

score 533 · Answer 11 · 2022-07-12 13:32:20

533

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Examples of non-Riemann integrable functions besides unbounded and Dirichlet functions.

Published on 12 Jul 2022 - 13:32

score 67 · Answer 12 · 2022-07-13 20:25:50

67

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A continuous nonnegative function with integral $0$ is identically $0$ (understanding why my approach is incorrect)

Published on 13 Jul 2022 - 20:25

score 1.5k · Answer 13 · 2022-07-13 20:56:07

1.5k

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If $f,g$ are continuous on $[a,b]$ and $g(x) > 0$ then there is a $c$ where $\int_{a}^{b} (fg)(x) dx = f(c) \int_{a}^{b} g(x) dx$

Published on 13 Jul 2022 - 20:56

score 98 · Answer 14 · 2022-07-15 13:49:53

98

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Prove function is Riemann Integrable

Published on 15 Jul 2022 - 13:49

score 158 · Answer 15 · 2022-07-16 05:53:32

158

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The Riemann–Stieltjes Integral: Proving a Convergence Theorem

Published on 16 Jul 2022 - 5:53

List Question

A special case of the Riemann–Stieltjes integral

Darboux integrability implies Riemann integrability in $\mathbb{R}^n$

Spivak's Calculus, Ch. 13 Appendix "Riemann Sums, Problem 3: Prove formula for length of parametric curve based on inscribed polygonal curve.

Potential problem with a proof involving Riemann Integral

What happens if you relax the "for all" requirement of Darboux integration?

For any $f\in C^1[0,1]$ show that $\sum_{k=1}^n f\big(\frac{k}{n}\big) - n \int_0^1 f(x)dx$ converges to $\frac{f(1)-f(0)}{2}$ as $n \to \infty$.

Prove or disprove: If $\int_0^1f(t)t^{2n+1}dt=0$ for each integer $n\geq 0$, then $f=0$ on $[0 ,1]$.

When is the indicator of a sublevel set integrable?

Problem in Riemann Summation method

Is there a function $f:[0,\infty) \to \{-1, 1\}$ such that $\int_0^\infty{f(x)\,dx}$ is well defined?

Examples of non-Riemann integrable functions besides unbounded and Dirichlet functions.

A continuous nonnegative function with integral $0$ is identically $0$ (understanding why my approach is incorrect)

If $f,g$ are continuous on $[a,b]$ and $g(x) > 0$ then there is a $c$ where $\int_{a}^{b} (fg)(x) dx = f(c) \int_{a}^{b} g(x) dx$

Prove function is Riemann Integrable

The Riemann–Stieltjes Integral: Proving a Convergence Theorem

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