Question

For what values of p the following integral converges: $\int_{1}^{\infty} \sin(x) \cdot x^p dx$

score 141 · Answer 1 · 2018-04-18 10:10:48

141

Views

For what values of p the following integral converges: $\int_{1}^{\infty} \sin(x) \cdot x^p dx$

Published on 18 Apr 2018 - 10:10

score 122 · Answer 2 · 2018-04-18 11:11:13

122

Views

$\int_0^{\infty} (-1)^{\lfloor{x^2}\rfloor} dx$ converges or diverges?

Published on 18 Apr 2018 - 11:11

score 410 · Answer 3 · 2026-03-25 06:13:12

410

Views

PV of $\int_{-\infty}^\infty \frac{x^n~ e^{-ax^2} dx}{(x-x_1)(x-x_2)},~ (n=0,1,2,3,...)$

Published on 25 Mar 2026 - 6:13

score 102 · Answer 4 · 2026-03-26 18:56:32

102

Views

Definite integral $\int_{y}^{\infty}$ involving two Meijer's G function

Published on 26 Mar 2026 - 18:56

score 54 · Answer 5 · 2018-04-19 09:05:59

54

Views

convergence of an improper integral, depending of a constant "a"

Published on 19 Apr 2018 - 9:05

score 61 · Answer 6 · 2018-04-19 17:19:03

61

Views

Change of variables in an integral

Published on 19 Apr 2018 - 17:19

score 1.1k · Answer 7 · 2018-04-19 18:12:04

1.1k

Views

Convergence of beta function

Published on 19 Apr 2018 - 18:12

score 81 · Answer 8 · 2026-03-25 05:50:49

81

Views

What went wrong with integrating $\frac {x^a}{1-x^b}$?

Published on 25 Mar 2026 - 5:50

score 893 · Answer 9 · 2018-04-20 14:24:20

893

Views

Limit of improper integral $ \lim_{x\to \infty} \ \int_1^x x\,e^{t^2-x^2} \,dt$

Published on 20 Apr 2018 - 14:24

score 68 · Answer 10 · 2018-04-20 15:50:06

68

Views

Prove that $\int_0^1 \frac{1}{x^\delta} \,dx$ convergent $\Leftrightarrow \ \delta <1$

Published on 20 Apr 2018 - 15:50

score 292 · Answer 11 · 2026-03-25 07:47:26

292

Views

Complex analysis: Improper integral of a non-even function

Published on 25 Mar 2026 - 7:47

score 86 · Answer 12 · 2026-03-25 13:52:56

86

Views

Integral with parameters, limit permutation and weak convergence in $L^2$

Published on 25 Mar 2026 - 13:52

score 329 · Answer 13 · 2026-03-25 07:44:36

329

Views

How a Definite Integral can have the same value as just of one of the points of the integration interval?

Published on 25 Mar 2026 - 7:44

score 58 · Answer 14 · 2026-03-25 04:36:09

58

Views

Convergence of Integrals - A Problem

Published on 25 Mar 2026 - 4:36

score 174 · Answer 15 · 2018-04-22 10:40:03

174

Views

Convergence of $\lim\limits_{n\to\infty}\frac{1}{n}\int_\limits{-n}^{n}\frac{1-e^{-nx^2}}{x^2(1+nx^2)}dx$

Published on 22 Apr 2018 - 10:40

List Question

For what values of p the following integral converges: $\int_{1}^{\infty} \sin(x) \cdot x^p dx$

$\int_0^{\infty} (-1)^{\lfloor{x^2}\rfloor} dx$ converges or diverges?

PV of $\int_{-\infty}^\infty \frac{x^n~ e^{-ax^2} dx}{(x-x_1)(x-x_2)},~ (n=0,1,2,3,...)$

Definite integral $\int_{y}^{\infty}$ involving two Meijer's G function

convergence of an improper integral, depending of a constant "a"

Change of variables in an integral

Convergence of beta function

What went wrong with integrating $\frac {x^a}{1-x^b}$?

Limit of improper integral $ \lim_{x\to \infty} \ \int_1^x x\,e^{t^2-x^2} \,dt$

Prove that $\int_0^1 \frac{1}{x^\delta} \,dx$ convergent $\Leftrightarrow \ \delta <1$

Complex analysis: Improper integral of a non-even function

Integral with parameters, limit permutation and weak convergence in $L^2$

How a Definite Integral can have the same value as just of one of the points of the integration interval?

Convergence of Integrals - A Problem

Convergence of $\lim\limits_{n\to\infty}\frac{1}{n}\int_\limits{-n}^{n}\frac{1-e^{-nx^2}}{x^2(1+nx^2)}dx$

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