Question

What is the term for this family of improper integrals?

score 291 · Answer 1 · 2026-03-29 18:32:28

291

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What is the term for this family of improper integrals?

Published on 29 Mar 2026 - 18:32

score 347 · Answer 2 · 2026-03-26 17:43:19

347

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Does Absolute Integrability Imply Riemann Integrability?

Published on 26 Mar 2026 - 17:43

score 112 · Answer 3 · 2018-11-14 23:25:41

112

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When is $\int_{-\infty}^\infty f(x) dx = \lim\limits_{n \to \infty} \int_{-n}^n f(x) dx$?

Published on 14 Nov 2018 - 23:25

score 143 · Answer 4 · 2018-11-15 20:11:53

143

Views

Similar to the Integral Test

Published on 15 Nov 2018 - 20:11

score 622 · Answer 5 · 2018-11-16 04:49:03

622

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Solving $\int_{0}^{\infty} \frac{\sin(x)}{x^3}dx$

Published on 16 Nov 2018 - 4:49

score 168 · Answer 6 · 2018-11-16 13:48:41

168

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Let $a_k\gt 0$ and $a_0\gt \sum_{k=1}^n a_k$ . Show that $\int_0^{\infty} \prod_{k=0}^n \frac {\sin (a_k x)}{x} dx=\frac {\pi}{2}\prod_{k=1}^n a_k$

Published on 16 Nov 2018 - 13:48

score 86 · Answer 7 · 2018-11-17 20:28:29

86

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prove if $f$ is bounded in [a,b] and integrable in every [a+$\epsilon$ , b] for every $\epsilon$ > 0 then $f$ integrable in [a,b]

Published on 17 Nov 2018 - 20:28

score 236 · Answer 8 · 2026-03-25 01:20:24

236

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Improper integral $\int_0^\infty \frac{x^{\alpha}\ln x}{x^2+1}\,dx=\frac{\pi^2}{4} \frac{\sin(\pi \alpha/2)}{\cos^2(\pi \alpha/2)}$

Published on 25 Mar 2026 - 1:20

score 357 · Answer 9 · 2026-03-26 04:38:04

357

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Why is the expectation of cauchy distribution not defined? (What is the intuition behind it?)

Published on 26 Mar 2026 - 4:38

score 1.4k · Answer 10 · 2026-03-26 17:47:42

1.4k

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Riemann integrability on open subset of $\mathbb{R}$

Published on 26 Mar 2026 - 17:47

score 40 · Answer 11 · 2026-03-26 17:43:37

40

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Integrability of bounded functions

Published on 26 Mar 2026 - 17:43

score 60 · Answer 12 · 2018-11-21 16:29:58

60

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Improper integral of a function

Published on 21 Nov 2018 - 16:29

score 52 · Answer 13 · 2026-03-25 01:17:36

52

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How to prove $\int_{-\infty}^\infty \frac{dx}{(e^x -x)^2 +\pi^2}=\frac{1}{1+W(1)}$?

Published on 25 Mar 2026 - 1:17

score 673 · Answer 14 · 2026-03-25 14:36:46

673

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$u(x,t)=\left(f*\mathcal{H}_{t}^{(n)}\right)(x)$ is solution to the n-dimensional heat equation

Published on 25 Mar 2026 - 14:36

score 35 · Answer 15 · 2018-11-21 22:59:15

35

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Finite integral and limit

Published on 21 Nov 2018 - 22:59

List Question

What is the term for this family of improper integrals?

Does Absolute Integrability Imply Riemann Integrability?

When is $\int_{-\infty}^\infty f(x) dx = \lim\limits_{n \to \infty} \int_{-n}^n f(x) dx$?

Similar to the Integral Test

Solving $\int_{0}^{\infty} \frac{\sin(x)}{x^3}dx$

Let $a_k\gt 0$ and $a_0\gt \sum_{k=1}^n a_k$ . Show that $\int_0^{\infty} \prod_{k=0}^n \frac {\sin (a_k x)}{x} dx=\frac {\pi}{2}\prod_{k=1}^n a_k$

prove if $f$ is bounded in [a,b] and integrable in every [a+$\epsilon$ , b] for every $\epsilon$ > 0 then $f$ integrable in [a,b]

Improper integral $\int_0^\infty \frac{x^{\alpha}\ln x}{x^2+1}\,dx=\frac{\pi^2}{4} \frac{\sin(\pi \alpha/2)}{\cos^2(\pi \alpha/2)}$

Why is the expectation of cauchy distribution not defined? (What is the intuition behind it?)

Riemann integrability on open subset of $\mathbb{R}$

Integrability of bounded functions

Improper integral of a function

How to prove $\int_{-\infty}^\infty \frac{dx}{(e^x -x)^2 +\pi^2}=\frac{1}{1+W(1)}$?

$u(x,t)=\left(f*\mathcal{H}_{t}^{(n)}\right)(x)$ is solution to the n-dimensional heat equation

Finite integral and limit

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