Question

Integral using the Substitution y = $\frac{1}{2}(\sqrt{a}x^2+\frac{\sqrt{b}}{x^2})$

score 78 · Answer 1 · 2026-03-25 01:37:04

78

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Integral using the Substitution y = $\frac{1}{2}(\sqrt{a}x^2+\frac{\sqrt{b}}{x^2})$

Published on 25 Mar 2026 - 1:37

score 354 · Answer 2 · 2018-05-31 07:30:18

354

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Does $\int_0^\infty \frac{\sin(\sin(x))}{x}dx$ converge or diverge?

Published on 31 May 2018 - 7:30

score 195 · Answer 3 · 2018-05-31 09:43:00

195

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If $I = \int_{-\infty}^\infty(xu - 3tu^2)\mathrm{d}x$, show that $\frac{\mathrm{d}I}{\mathrm{d}t} = 0$.

Published on 31 May 2018 - 9:43

score 51 · Answer 4 · 2026-03-26 12:35:01

51

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Question regarding the definition of improper integral.

Published on 26 Mar 2026 - 12:35

score 351 · Answer 5 · 2018-05-31 19:23:01

351

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If $\int_{1}^{\infty}f\left(x\right)dx$ converges absolutely then $\int_{1}^{\infty}f^{2}\left(x\right)dx$ converges?

Published on 31 May 2018 - 19:23

score 231 · Answer 6 · 2018-05-31 19:46:36

231

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Uniform convergence of improper integrals with squared integrand

Published on 31 May 2018 - 19:46

score 298 · Answer 7 · 2018-05-31 19:55:15

298

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Is this a proof that $\operatorname{Si}(x)$ is well-defined, continuous and bounded?

Published on 31 May 2018 - 19:55

score 150 · Answer 8 · 2018-06-01 17:36:09

150

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Evaluate $\int_1^{\infty} \frac {(\{x\}-\frac 12)dx}{x}$

Published on 01 Jun 2018 - 17:36

score 90 · Answer 9 · 2026-03-25 23:20:44

90

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Order of Integration in Divergent Integrals

Published on 25 Mar 2026 - 23:20

score 274 · Answer 10 · 2018-06-02 14:30:36

274

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Convergence of improper integral $\to\pi$

Published on 02 Jun 2018 - 14:30

score 79 · Answer 11 · 2018-06-02 14:40:20

79

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Prove convergence of an improper integral.

Published on 02 Jun 2018 - 14:40

score 128 · Answer 12 · 2018-06-02 18:49:27

128

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computing $\int_{-\infty}^{\infty}\frac{x^3\sin(ax)}{x^4+b^4}$

Published on 02 Jun 2018 - 18:49

score 68 · Answer 13 · 2018-06-03 23:12:09

68

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Prove $\lim_{y \to 0^+} \frac{y}{\pi} \int_{-\infty}^{+\infty} \frac{f(x) \, \mathrm{d}x}{x^2+y^2} = f(0)$ with $f$ continuous, bounded

Published on 03 Jun 2018 - 23:12

score 206 · Answer 14 · 2018-06-05 03:56:33

206

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Convergence of an improper integral of two variables

Published on 05 Jun 2018 - 3:56

score 99 · Answer 15 · 2018-06-05 10:12:05

99

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Necessary condition for an improper integral of two variables to converge

Published on 05 Jun 2018 - 10:12

List Question

Integral using the Substitution y = $\frac{1}{2}(\sqrt{a}x^2+\frac{\sqrt{b}}{x^2})$

Does $\int_0^\infty \frac{\sin(\sin(x))}{x}dx$ converge or diverge?

If $I = \int_{-\infty}^\infty(xu - 3tu^2)\mathrm{d}x$, show that $\frac{\mathrm{d}I}{\mathrm{d}t} = 0$.

Question regarding the definition of improper integral.

If $\int_{1}^{\infty}f\left(x\right)dx$ converges absolutely then $\int_{1}^{\infty}f^{2}\left(x\right)dx$ converges?

Uniform convergence of improper integrals with squared integrand

Is this a proof that $\operatorname{Si}(x)$ is well-defined, continuous and bounded?

Evaluate $\int_1^{\infty} \frac {(\{x\}-\frac 12)dx}{x}$

Order of Integration in Divergent Integrals

Convergence of improper integral $\to\pi$

Prove convergence of an improper integral.

computing $\int_{-\infty}^{\infty}\frac{x^3\sin(ax)}{x^4+b^4}$

Prove $\lim_{y \to 0^+} \frac{y}{\pi} \int_{-\infty}^{+\infty} \frac{f(x) \, \mathrm{d}x}{x^2+y^2} = f(0)$ with $f$ continuous, bounded

Convergence of an improper integral of two variables

Necessary condition for an improper integral of two variables to converge

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