Question

General condition that Riemann and Lebesgue integrals are the same

score 8.9k · Answer 1 · 2026-03-26 12:35:22

8.9k

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General condition that Riemann and Lebesgue integrals are the same

Published on 26 Mar 2026 - 12:35

score 926 · Answer 2 · 2014-06-11 02:53:07

926

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A simple convergent integral but not absolutely convergent.

Published on 11 Jun 2014 - 2:53

score 109 · Answer 3 · 2014-06-11 09:16:50

109

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Find the value of $a$ if $\int_0^\infty \frac{2x}{a}e^{\Large\frac{-x^2}{a}}\ dx=1 $

Published on 11 Jun 2014 - 9:16

score 64 · Answer 4 · 2014-06-11 09:26:10

64

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How to prove the non existence of this integral?

Published on 11 Jun 2014 - 9:26

score 196 · Answer 5 · 2026-03-30 05:30:11

196

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Evaluate $\int_{0}^{\infty}\sqrt{\frac{ a^2 -y^2 + \sqrt{(a^2-y^2)^2+4y^2} }{(a^2-y^2)^2+4y^2}}dy=\sqrt{2}\pi$

Published on 30 Mar 2026 - 5:30

score 2k · Answer 6 · 2014-06-11 16:45:14

2k

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Evaluate $\int_0^{\infty}\int_0^{\infty}e^{-x^2-2xy-y^2}\,dx\,dy$

Published on 11 Jun 2014 - 16:45

score 16k · Answer 7 · 2014-06-12 00:16:14

16k

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Intuitively, why does $\int_{-\infty}^{\infty}\sin(x)dx$ diverge?

Published on 12 Jun 2014 - 0:16

score 2.3k · Answer 8 · 2026-03-28 03:34:49

2.3k

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How to evaluate improper integral $\int_{0}^{\infty}\frac{\tan^{-1}{x}}{e^{ax}-1}dx$?

Published on 28 Mar 2026 - 3:34

score 62 · Answer 9 · 2014-06-12 09:15:09

62

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Calculating integral with different boundary

Published on 12 Jun 2014 - 9:15

score 129 · Answer 10 · 2014-06-12 11:11:27

129

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Convergence of $\displaystyle\int\frac{1}{\sqrt[3]{1-x^3}}\ dx$

Published on 12 Jun 2014 - 11:11

score 248 · Answer 11 · 2026-03-26 13:51:38

248

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Show that $\int_{-\infty}^{\infty}\frac{x^2dx}{(x^2+1)^2(x^2+2x+2)}=\frac{7\pi}{50}$

Published on 26 Mar 2026 - 13:51

score 211 · Answer 12 · 2014-06-14 09:21:26

211

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Limit of an integral $\int_0^{\pi/2} \frac{x\sin^nx}{\sqrt{1+\sin^2 x}}\ dx$

Published on 14 Jun 2014 - 9:21

score 66 · Answer 13 · 2014-06-14 14:43:30

66

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Difficult integrals, do they converge, show there's no dependence on parameters.

Published on 14 Jun 2014 - 14:43

score 239 · Answer 14 · 2014-06-14 19:19:30

How to show that $\int_{-\infty}^\infty\frac{t}{(a^2+t^2)(b^2+t^2)(e^{2\pi t}-1)}dt=\frac{1}{2ab(a+b)}+\frac{1}{b^2-a^2}\sum_{a<k\leq b}\frac{1}{k}$

score 130 · Answer 15 · 2014-06-14 22:14:16

130

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An improper integral question

Published on 14 Jun 2014 - 22:14

List Question

General condition that Riemann and Lebesgue integrals are the same

A simple convergent integral but not absolutely convergent.

Find the value of $a$ if $\int_0^\infty \frac{2x}{a}e^{\Large\frac{-x^2}{a}}\ dx=1 $

How to prove the non existence of this integral?

Evaluate $\int_{0}^{\infty}\sqrt{\frac{ a^2 -y^2 + \sqrt{(a^2-y^2)^2+4y^2} }{(a^2-y^2)^2+4y^2}}dy=\sqrt{2}\pi$

Evaluate $\int_0^{\infty}\int_0^{\infty}e^{-x^2-2xy-y^2}\,dx\,dy$

Intuitively, why does $\int_{-\infty}^{\infty}\sin(x)dx$ diverge?

How to evaluate improper integral $\int_{0}^{\infty}\frac{\tan^{-1}{x}}{e^{ax}-1}dx$?

Calculating integral with different boundary

Convergence of $\displaystyle\int\frac{1}{\sqrt[3]{1-x^3}}\ dx$

Show that $\int_{-\infty}^{\infty}\frac{x^2dx}{(x^2+1)^2(x^2+2x+2)}=\frac{7\pi}{50}$

Limit of an integral $\int_0^{\pi/2} \frac{x\sin^nx}{\sqrt{1+\sin^2 x}}\ dx$

Difficult integrals, do they converge, show there's no dependence on parameters.

How to show that $\int_{-\infty}^\infty\frac{t}{(a^2+t^2)(b^2+t^2)(e^{2\pi t}-1)}dt=\frac{1}{2ab(a+b)}+\frac{1}{b^2-a^2}\sum_{a<k\leq b}\frac{1}{k}$

An improper integral question

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