Question

If $ \ \lim_{|x| \to \infty} f(x)=0=\lim_{|x| \to \infty} g(x) \ $ , then $ \ |f|^2 , \ |g|^2 \ $ also have finite integrals

score 33 · Answer 1 · 2018-05-20 23:56:03

33

Views

If $ \ \lim_{|x| \to \infty} f(x)=0=\lim_{|x| \to \infty} g(x) \ $ , then $ \ |f|^2 , \ |g|^2 \ $ also have finite integrals

Published on 20 May 2018 - 23:56

score 465 · Answer 2 · 2018-05-21 02:02:44

465

Views

Evaluate $\int_0^{\pi/2}\ln^2(\sin\theta)\,\mathrm d\theta$

Published on 21 May 2018 - 2:02

score 214 · Answer 3 · 2018-05-21 10:43:09

214

Views

Evaluate improper integral

Published on 21 May 2018 - 10:43

score 409 · Answer 4 · 2026-03-25 06:12:10

409

Views

Evaluate $\int_{0}^{\infty} \frac{x \exp\left\{-\beta^2 x^2\right\}}{\sinh \left(\frac{\pi x}{2}\right)} \mathrm{d} x$

Published on 25 Mar 2026 - 6:12

score 236 · Answer 5 · 2026-03-25 18:46:30

236

Views

Residue theorem and incomplete Gamma functions

Published on 25 Mar 2026 - 18:46

score 93 · Answer 6 · 2026-03-27 00:57:15

93

Views

Prove $\int_\limits{0}^{\infty} n^4 t^2e^{-2nt} dt$ divergence

Published on 27 Mar 2026 - 0:57

score 41 · Answer 7 · 2018-05-22 19:21:39

41

Views

convergence of improper-integral

Published on 22 May 2018 - 19:21

score 131 · Answer 8 · 2018-05-23 05:56:55

131

Views

Solving integral $\int \int _{\Bbb{R}^2} e^{-(3x+2y)^2 - (4x+y)^2} dx dy$?

Published on 23 May 2018 - 5:56

score 97 · Answer 9 · 2026-03-25 08:09:39

97

Views

Evaluate: $\int_{0}^{\infty}\frac{\ln^{n}(x)\ln(1+x)}{x(1+x^2)}\mathrm dx$

Published on 25 Mar 2026 - 8:09

score 1.1k · Answer 10 · 2026-03-25 17:35:03

1.1k

Views

improper integral trapezoid and simpson rule

Published on 25 Mar 2026 - 17:35

score 243 · Answer 11 · 2018-05-23 17:49:36

243

Views

Derivative of an improper integral

Published on 23 May 2018 - 17:49

score 240 · Answer 12 · 2018-05-23 20:12:21

240

Views

Does $\int _1^{\infty }\left(\arctan\left(e^x\right)-\frac{\pi }{2}\:\right)\:dx$ converge?

Published on 23 May 2018 - 20:12

score 49 · Answer 13 · 2018-05-24 09:14:42

49

Views

Prove convergence by bounding with another function

Published on 24 May 2018 - 9:14

score 54 · Answer 14 · 2018-05-24 12:39:32

54

Views

Convergence of integral with trigonometry

Published on 24 May 2018 - 12:39

score 164 · Answer 15 · 2026-03-26 01:09:40

164

Views

$2$ equal improper integrals but one integral converges absolutely other is not

Published on 26 Mar 2026 - 1:09

List Question

If $ \ \lim_{|x| \to \infty} f(x)=0=\lim_{|x| \to \infty} g(x) \ $ , then $ \ |f|^2 , \ |g|^2 \ $ also have finite integrals

Evaluate $\int_0^{\pi/2}\ln^2(\sin\theta)\,\mathrm d\theta$

Evaluate improper integral

Evaluate $\int_{0}^{\infty} \frac{x \exp\left\{-\beta^2 x^2\right\}}{\sinh \left(\frac{\pi x}{2}\right)} \mathrm{d} x$

Residue theorem and incomplete Gamma functions

Prove $\int_\limits{0}^{\infty} n^4 t^2e^{-2nt} dt$ divergence

convergence of improper-integral

Solving integral $\int \int _{\Bbb{R}^2} e^{-(3x+2y)^2 - (4x+y)^2} dx dy$?

Evaluate: $\int_{0}^{\infty}\frac{\ln^{n}(x)\ln(1+x)}{x(1+x^2)}\mathrm dx$

improper integral trapezoid and simpson rule

Derivative of an improper integral

Does $\int _1^{\infty }\left(\arctan\left(e^x\right)-\frac{\pi }{2}\:\right)\:dx$ converge?

Prove convergence by bounding with another function

Convergence of integral with trigonometry

$2$ equal improper integrals but one integral converges absolutely other is not

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