Question

Evaluating the integral $ \int_0^{\infty} \cos(x^2)\, \mathrm{d} x$?

score 363 · Answer 1 · 2014-10-13 05:09:31

363

Views

Evaluating the integral $ \int_0^{\infty} \cos(x^2)\, \mathrm{d} x$?

Published on 13 Oct 2014 - 5:09

score 21 · Answer 2 · 2014-10-13 12:25:48

21

Views

Is it always true that an integral diverges on (a,b) if it diverges on (c,b) and a<c<b?

Published on 13 Oct 2014 - 12:25

score 296 · Answer 3 · 2026-03-28 16:56:28

296

Views

Tempered distribution and primitive integral

Published on 28 Mar 2026 - 16:56

score 791 · Answer 4 · 2026-03-29 12:05:30

791

Views

How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$

Published on 29 Mar 2026 - 12:05

score 105 · Answer 5 · 2014-10-16 01:15:50

105

Views

Determine whether $\lim_{R\to\infty}\int_0^R\frac{|\sin x|}{x}dx-\frac{2}{\pi}\ln R$ exists

Published on 16 Oct 2014 - 1:15

score 138 · Answer 6 · 2026-03-28 01:12:56

138

Views

Why do we care about the 'rapidness' for convergence?

Published on 28 Mar 2026 - 1:12

score 617 · Answer 7 · 2014-10-16 18:45:56

617

Views

Prove that $\int_{0}^{+\infty} u^{s-1} \cos (a u) \:e^{-b u}\:du=\frac{\Gamma(s)\cos\left(s\arctan \left(\frac{a}{b}\right)\right)}{(a^2+b^2)^{s/2}}$

Published on 16 Oct 2014 - 18:45

score 153 · Answer 8 · 2014-10-17 00:24:27

153

Views

Cauchy Principal Value different from the improper integral

Published on 17 Oct 2014 - 0:24

score 73 · Answer 9 · 2014-10-17 03:09:33

73

Views

inverse fourier transform of exponencial

Published on 17 Oct 2014 - 3:09

score 2.3k · Answer 10 · 2014-10-17 06:25:25

2.3k

Views

Integral test error approximation

Published on 17 Oct 2014 - 6:25

score 3.5k · Answer 11 · 2026-03-29 12:05:14

3.5k

Views

Evaluating $\int_0^\infty \frac{dx}{\sqrt{x}[x^2+(1+2\sqrt{2})x+1][1-x+x^2-x^3+...+x^{50}]}$

Published on 29 Mar 2026 - 12:05

score 66 · Answer 12 · 2014-10-18 13:40:23

66

Views

How to prove this multivariable integral identity?

Published on 18 Oct 2014 - 13:40

score 1.1k · Answer 13 · 2014-10-19 03:36:36

1.1k

Views

Find the Values of $p$ and $q$ such that $\int_0^{\infty} x^p\ln(1+x)^q dx$ Converges or Diverges.

Published on 19 Oct 2014 - 3:36

score 6.8k · Answer 14 · 2014-10-19 08:23:58

6.8k

Views

Some integral representations of the Euler–Mascheroni constant

Published on 19 Oct 2014 - 8:23

score 173 · Answer 15 · 2014-10-19 17:18:19

173

Views

Does $\int_{3}^{\infty}\frac{1}{(x-2)^{3/2}}\text{ d}x$ converge?

Published on 19 Oct 2014 - 17:18

List Question

Evaluating the integral $ \int_0^{\infty} \cos(x^2)\, \mathrm{d} x$?

Is it always true that an integral diverges on (a,b) if it diverges on (c,b) and a<c<b?

Tempered distribution and primitive integral

How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$

Determine whether $\lim_{R\to\infty}\int_0^R\frac{|\sin x|}{x}dx-\frac{2}{\pi}\ln R$ exists

Why do we care about the 'rapidness' for convergence?

Prove that $\int_{0}^{+\infty} u^{s-1} \cos (a u) \:e^{-b u}\:du=\frac{\Gamma(s)\cos\left(s\arctan \left(\frac{a}{b}\right)\right)}{(a^2+b^2)^{s/2}}$

Cauchy Principal Value different from the improper integral

inverse fourier transform of exponencial

Integral test error approximation

Evaluating $\int_0^\infty \frac{dx}{\sqrt{x}[x^2+(1+2\sqrt{2})x+1][1-x+x^2-x^3+...+x^{50}]}$

How to prove this multivariable integral identity?

Find the Values of $p$ and $q$ such that $\int_0^{\infty} x^p\ln(1+x)^q dx$ Converges or Diverges.

Some integral representations of the Euler–Mascheroni constant

Does $\int_{3}^{\infty}\frac{1}{(x-2)^{3/2}}\text{ d}x$ converge?

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