Question

Is the Laplace transform of $f(-t)$ given by $F(-s)$?

score 1k · Answer 1 · 2026-03-26 20:16:52

1k

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Is the Laplace transform of $f(-t)$ given by $F(-s)$?

Published on 26 Mar 2026 - 20:16

score 101 · Answer 2 · 2018-06-23 12:34:01

101

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For which values of the parameter $\beta$ is the following integral convergent

Published on 23 Jun 2018 - 12:34

score 162 · Answer 3 · 2018-06-24 03:53:24

162

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Problem: To show that $\int_{0}^{\infty}\sqrt[3]{(e^x-1)^2}\cdot \frac{dx}{1-2\cosh x}=-\frac{4}{3}\pi\sin\left(\frac{2}{9}\pi\right)$

Published on 24 Jun 2018 - 3:53

score 110 · Answer 4 · 2026-03-26 22:13:14

110

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How do you memorize Abel and Dirichlet convergence criterions?

Published on 26 Mar 2026 - 22:13

score 202 · Answer 5 · 2026-03-25 01:18:45

202

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Check proof of $\int_{0}^{\infty}\sin(x\sinh\alpha)\sin(x\cosh\alpha)\ln(x)\frac{dx}{x}=-\alpha\gamma$

Published on 25 Mar 2026 - 1:18

score 1k · Answer 6 · 2018-06-25 13:45:34

1k

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Improper integral of product of functions

Published on 25 Jun 2018 - 13:45

score 129 · Answer 7 · 2018-06-25 15:20:21

129

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For which values of $p,q$, does the following double integral converge?

Published on 25 Jun 2018 - 15:20

score 222 · Answer 8 · 2018-06-25 15:35:07

222

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Evaluate $\int_{-\infty}^\infty e^{x/2}\operatorname{sech}(x)\,dx$ without Residue Calculus

Published on 25 Jun 2018 - 15:35

score 182 · Answer 9 · 2026-03-26 19:15:50

182

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Improper integrals with residue theorem

Published on 26 Mar 2026 - 19:15

score 54 · Answer 10 · 2018-06-27 08:23:07

54

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Integral with log and sin

Published on 27 Jun 2018 - 8:23

score 177 · Answer 11 · 2026-03-26 06:15:12

177

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Proving that $\int_A f = \underline \int_Q f_A$ for a non-negative function defined on an open subset $A$ of $\mathbb{R}^n$

Published on 26 Mar 2026 - 6:15

score 63 · Answer 12 · 2018-06-29 10:25:51

63

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$ \lim_{c \to a} \int_0^c f(x,c) \space dx $

Published on 29 Jun 2018 - 10:25

score 1.6k · Answer 13 · 2018-06-29 12:02:29

1.6k

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Fubini's theorem and the Gaussian Integral

Published on 29 Jun 2018 - 12:02

score 92 · Answer 14 · 2026-03-25 04:41:12

92

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Show that $\int_0^{\infty} (\exp(x) - 2^{\sqrt 5 +1} + 1) (\coth(x) - 1) x^{\sqrt 5} dx = 0 $

Published on 25 Mar 2026 - 4:41

score 85 · Answer 15 · 2018-06-30 17:32:41

85

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If $\int_a^\infty f(x) dx$ converges, does there exist $0<c<1$ such that for $c \le p \le 1,$ $\int_a^\infty f^p(x)$ converges?

Published on 30 Jun 2018 - 17:32

List Question

Is the Laplace transform of $f(-t)$ given by $F(-s)$?

For which values of the parameter $\beta$ is the following integral convergent

Problem: To show that $\int_{0}^{\infty}\sqrt[3]{(e^x-1)^2}\cdot \frac{dx}{1-2\cosh x}=-\frac{4}{3}\pi\sin\left(\frac{2}{9}\pi\right)$

How do you memorize Abel and Dirichlet convergence criterions?

Check proof of $\int_{0}^{\infty}\sin(x\sinh\alpha)\sin(x\cosh\alpha)\ln(x)\frac{dx}{x}=-\alpha\gamma$

Improper integral of product of functions

For which values of $p,q$, does the following double integral converge?

Evaluate $\int_{-\infty}^\infty e^{x/2}\operatorname{sech}(x)\,dx$ without Residue Calculus

Improper integrals with residue theorem

Integral with log and sin

Proving that $\int_A f = \underline \int_Q f_A$ for a non-negative function defined on an open subset $A$ of $\mathbb{R}^n$

$ \lim_{c \to a} \int_0^c f(x,c) \space dx $

Fubini's theorem and the Gaussian Integral

Show that $\int_0^{\infty} (\exp(x) - 2^{\sqrt 5 +1} + 1) (\coth(x) - 1) x^{\sqrt 5} dx = 0 $

If $\int_a^\infty f(x) dx$ converges, does there exist $0<c<1$ such that for $c \le p \le 1,$ $\int_a^\infty f^p(x)$ converges?

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