Question

Approximating Darboux integrals with continuous functions

score 304 · Answer 1 · 2026-03-25 20:32:36

304

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Approximating Darboux integrals with continuous functions

Published on 25 Mar 2026 - 20:32

score 532 · Answer 2 · 2018-10-27 18:28:58

532

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Can a function f be Riemann integrable over an open interval? Or does the interval considered always need to be closed?

Published on 27 Oct 2018 - 18:28

score 717 · Answer 3 · 2018-10-29 01:44:53

717

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Is $\frac {\sin^2(x)}{x^2}$ Lebesgue integrable on $[0,\infty)$?

Published on 29 Oct 2018 - 1:44

score 45 · Answer 4 · 2026-02-23 04:14:49

45

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Solving the integral of a step function

Published on 23 Feb 2026 - 4:14

score 164 · Answer 5 · 2026-03-25 17:43:57

164

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A question regarding two Cauchy definitions of integrability

Published on 25 Mar 2026 - 17:43

score 2.9k · Answer 6 · 2018-10-31 12:53:56

2.9k

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Under what circumstances is a characteristic function Riemann integrable?

Published on 31 Oct 2018 - 12:53

score 672 · Answer 7 · 2026-03-25 06:04:53

672

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What is the Sigma Algebra generated by Jordan measurable sets?

Published on 25 Mar 2026 - 6:04

score 97 · Answer 8 · 2018-11-01 18:24:53

97

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$t \in \mathbb{R}$ so that $f(t)=\int_{0}^{+\infty}e^{-tx}\frac{\sin x}{x}dx, t\in\mathbb{R}$ exists

Published on 01 Nov 2018 - 18:24

score 44 · Answer 9 · 2018-11-02 14:55:12

44

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$t \in \mathbb{R}$ s.t. $f(t)=\int_{0}^{+\infty}\sin(x^t) \ dx, t\in\mathbb{R}$ exists

Published on 02 Nov 2018 - 14:55

score 246 · Answer 10 · 2018-11-02 18:20:39

246

Views

equivalent statements about a real integrable function $f:[a,b]\to\mathbb R$

Published on 02 Nov 2018 - 18:20

score 96 · Answer 11 · 2018-11-02 19:53:32

96

Views

$\varphi$ is integrable if and only if $f=g$

Published on 02 Nov 2018 - 19:53

score 168 · Answer 12 · 2018-11-02 20:04:55

168

Views

Continuous function with 2 discontinuous points is Riemann integrable

Published on 02 Nov 2018 - 20:04

score 138 · Answer 13 · 2018-11-03 00:05:13

138

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$f:\mathbb R\to\mathbb R$ differentiable, $f(0)=0$ and $f'(x)=[f(x)]^2$. Prove that $f(x)=0$ for all $x\in\mathbb R$.

Published on 03 Nov 2018 - 0:05

score 177 · Answer 14 · 2018-11-03 02:51:39

177

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Prove that $\underline{\int_a^b} f(x)dx=\sup_{\xi}\int_a^b \xi(x)dx$, $\xi$ a step-function.

Published on 03 Nov 2018 - 2:51

score 35 · Answer 15 · 2018-11-03 04:56:49

35

Views

Riemann Integrable.

Published on 03 Nov 2018 - 4:56

List Question

Approximating Darboux integrals with continuous functions

Can a function f be Riemann integrable over an open interval? Or does the interval considered always need to be closed?

Is $\frac {\sin^2(x)}{x^2}$ Lebesgue integrable on $[0,\infty)$?

Solving the integral of a step function

A question regarding two Cauchy definitions of integrability

Under what circumstances is a characteristic function Riemann integrable?

What is the Sigma Algebra generated by Jordan measurable sets?

$t \in \mathbb{R}$ so that $f(t)=\int_{0}^{+\infty}e^{-tx}\frac{\sin x}{x}dx, t\in\mathbb{R}$ exists

$t \in \mathbb{R}$ s.t. $f(t)=\int_{0}^{+\infty}\sin(x^t) \ dx, t\in\mathbb{R}$ exists

equivalent statements about a real integrable function $f:[a,b]\to\mathbb R$

$\varphi$ is integrable if and only if $f=g$

Continuous function with 2 discontinuous points is Riemann integrable

$f:\mathbb R\to\mathbb R$ differentiable, $f(0)=0$ and $f'(x)=[f(x)]^2$. Prove that $f(x)=0$ for all $x\in\mathbb R$.

Prove that $\underline{\int_a^b} f(x)dx=\sup_{\xi}\int_a^b \xi(x)dx$, $\xi$ a step-function.

Riemann Integrable.

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