Question

Find p values so that improper integrals converge

score 122 · Answer 1 · 2018-05-25 11:18:11

122

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Find p values so that improper integrals converge

Published on 25 May 2018 - 11:18

score 106 · Answer 2 · 2018-05-26 05:51:38

106

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Prove that $\int\limits_{x}^{+\infty}\frac{ds}{1+s^2}\geq \frac{x}{1+x^2},~x\geq 0.$

Published on 26 May 2018 - 5:51

score 59 · Answer 3 · 2018-05-26 05:57:24

59

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Prove or disprove: $\int\limits_{0}^{+\infty}\frac{e^{-x}}{1+ax}\,dx=1-a,~~0<a<1.$

Published on 26 May 2018 - 5:57

score 139 · Answer 4 · 2026-03-25 20:12:52

139

Views

Upper bound in an integral with exponential

Published on 25 Mar 2026 - 20:12

score 252 · Answer 5 · 2018-05-27 15:25:05

252

Views

the convergence of $\int_0^\infty t^{2k}e^{-xt^2}dt $ being uniform on $[\delta,\infty)$ for $\delta\gt 0$

Published on 27 May 2018 - 15:25

score 240 · Answer 6 · 2026-03-25 20:13:54

240

Views

Compute $\int_0^{+\infty}\frac{x^{\alpha}}{1+x^n}dx$, $0<1+\alpha<n$

Published on 25 Mar 2026 - 20:13

score 84 · Answer 7 · 2018-05-28 05:37:09

84

Views

Compute $\int_{0}^{\infty} \frac{\sqrt{x}}{(1+x)^2} dx$

Published on 28 May 2018 - 5:37

score 758 · Answer 8 · 2026-03-25 20:15:50

758

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Prove that $\int\limits_{-\infty}^{\infty} \frac{e^{-x}}{1+e^{-2\pi x}}\,dx=\frac1{2\sin\left(\frac{1}{2}\right)}$

Published on 25 Mar 2026 - 20:15

score 1.9k · Answer 9 · 2026-03-26 11:06:08

1.9k

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Fourier transform of function $f(x)$

Published on 26 Mar 2026 - 11:06

score 966 · Answer 10 · 2026-03-26 11:04:54

966

Views

What is the fourier transform of $e^{-\frac{t^2}2}$

Published on 26 Mar 2026 - 11:04

score 102 · Answer 11 · 2018-05-28 17:23:16

102

Views

Convergence or divergence of the integral $\int\limits_{10}^\infty \frac{e^x}{x^{1 + \frac{1}{x}} (e^x -1)} \,dx$

Published on 28 May 2018 - 17:23

score 696 · Answer 12 · 2026-03-25 12:55:03

696

Views

Class of integrals: $I(a)=\int_0^\infty \frac{dx}{e^x+ax}$

Published on 25 Mar 2026 - 12:55

score 132 · Answer 13 · 2018-05-30 08:34:26

132

Views

For what range of $n$ does improper integral $\int_0^{+\infty}\frac{\arctan(x)}{x^n}dx$ converge

Published on 30 May 2018 - 8:34

score 214 · Answer 14 · 2018-05-30 10:04:22

214

Views

Calculate $\int_{-\infty}^{\infty}\frac{e^{-i x}}{x^2+1}dx$ using residue theorem

Published on 30 May 2018 - 10:04

score 277 · Answer 15 · 2026-03-22 07:21:55

277

Views

Integrals of motion remain constant (proof)

Published on 22 Mar 2026 - 7:21

List Question

Find p values so that improper integrals converge

Prove that $\int\limits_{x}^{+\infty}\frac{ds}{1+s^2}\geq \frac{x}{1+x^2},~x\geq 0.$

Prove or disprove: $\int\limits_{0}^{+\infty}\frac{e^{-x}}{1+ax}\,dx=1-a,~~0<a<1.$

Upper bound in an integral with exponential

the convergence of $\int_0^\infty t^{2k}e^{-xt^2}dt $ being uniform on $[\delta,\infty)$ for $\delta\gt 0$

Compute $\int_0^{+\infty}\frac{x^{\alpha}}{1+x^n}dx$, $0<1+\alpha<n$

Compute $\int_{0}^{\infty} \frac{\sqrt{x}}{(1+x)^2} dx$

Prove that $\int\limits_{-\infty}^{\infty} \frac{e^{-x}}{1+e^{-2\pi x}}\,dx=\frac1{2\sin\left(\frac{1}{2}\right)}$

Fourier transform of function $f(x)$

What is the fourier transform of $e^{-\frac{t^2}2}$

Convergence or divergence of the integral $\int\limits_{10}^\infty \frac{e^x}{x^{1 + \frac{1}{x}} (e^x -1)} \,dx$

Class of integrals: $I(a)=\int_0^\infty \frac{dx}{e^x+ax}$

For what range of $n$ does improper integral $\int_0^{+\infty}\frac{\arctan(x)}{x^n}dx$ converge

Calculate $\int_{-\infty}^{\infty}\frac{e^{-i x}}{x^2+1}dx$ using residue theorem

Integrals of motion remain constant (proof)

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