Question

Techniques to prove the monotonicity of an integral as a function of parameter

score 31 · Answer 1 · 2026-04-11 01:38:27

31

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Techniques to prove the monotonicity of an integral as a function of parameter

Published on 11 Apr 2026 - 1:38

score 281 · Answer 2 · 2026-04-17 13:46:09

281

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Estimating $\int_0^1 a^x\ \frac{x(1-x)}{\sin(\pi x)} dx$

Published on 17 Apr 2026 - 13:46

score 190 · Answer 3 · 2026-04-13 12:41:56

190

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How to deal with a substitution that makes both the limits/bounds of an integral tending to infinity?

Published on 13 Apr 2026 - 12:41

score 283 · Answer 4 · 2026-04-16 08:01:48

283

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Show $\frac{\pi^2}{6}\sqrt{ab+\sqrt{ab+2\sqrt{ab+3\sqrt{\cdots}}}}>4$ by hand .

Published on 16 Apr 2026 - 8:01

score 38 · Answer 5 · 2026-04-12 23:44:36

38

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Can an improper integral with infinity singularity converge for any integrand?

Published on 12 Apr 2026 - 23:44

score 147 · Answer 6 · 2026-04-17 02:36:34

147

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Closed-form for $\int_0^\infty \frac{a}{x}\sqrt{x^2+\frac{a^2}{x^2}} \exp\left(-x^2-\frac{a^2}{x^2}\right)dx$

Published on 17 Apr 2026 - 2:36

score 93 · Answer 7 · 2026-04-17 06:07:15

93

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Calculating $\int_0^1 2x \sin⁡(1/x^2 )-2/x \cos⁡(1/x^2 ) dx$

Published on 17 Apr 2026 - 6:07

score 126 · Answer 8 · 2026-04-14 08:34:39

126

Views

(Dis)Prove that the two integrals are equal

Published on 14 Apr 2026 - 8:34

score 66 · Answer 9 · 2026-04-15 20:24:03

66

Views

Calculate the area between $f(x) = x \cos^2(x)$ and $g(x) = x$

Published on 15 Apr 2026 - 20:24

score 73 · Answer 10 · 2026-04-12 10:32:38

73

Views

A variation of Dirichlet's test for improper integrals

Published on 12 Apr 2026 - 10:32

score 86 · Answer 11 · 2026-04-13 12:58:40

86

Views

Improper integrals divergence\convergence

Published on 13 Apr 2026 - 12:58

score 121 · Answer 12 · 2026-04-11 15:20:59

121

Views

Improper integral convergence implies the existence of an infinite series which its partial sum converges

Published on 11 Apr 2026 - 15:20

score 96 · Answer 13 · 2026-04-15 23:41:44

Proving that $\int_1^{\infty} \frac{e^{-2at}}{\sqrt{{t-\frac{1}{t}}}} dt = \sqrt{\frac{a}{\pi}}\,\mathrm{K}_{\frac34}(a) \,\mathrm{K}_{\frac14}(a)$

score 81 · Answer 14 · 2026-04-10 00:26:22

81

Views

Confusion regarding indefinite integral

Published on 10 Apr 2026 - 0:26

score 273 · Answer 15 · 2026-04-10 14:10:48

273

Views

Double Limits When Defining Improper Integral

Published on 10 Apr 2026 - 14:10

List Question

Techniques to prove the monotonicity of an integral as a function of parameter

Estimating $\int_0^1 a^x\ \frac{x(1-x)}{\sin(\pi x)} dx$

How to deal with a substitution that makes both the limits/bounds of an integral tending to infinity?

Show $\frac{\pi^2}{6}\sqrt{ab+\sqrt{ab+2\sqrt{ab+3\sqrt{\cdots}}}}>4$ by hand .

Can an improper integral with infinity singularity converge for any integrand?

Closed-form for $\int_0^\infty \frac{a}{x}\sqrt{x^2+\frac{a^2}{x^2}} \exp\left(-x^2-\frac{a^2}{x^2}\right)dx$

Calculating $\int_0^1 2x \sin⁡(1/x^2 )-2/x \cos⁡(1/x^2 ) dx$

(Dis)Prove that the two integrals are equal

Calculate the area between $f(x) = x \cos^2(x)$ and $g(x) = x$

A variation of Dirichlet's test for improper integrals

Improper integrals divergence\convergence

Improper integral convergence implies the existence of an infinite series which its partial sum converges

Proving that $\int_1^{\infty} \frac{e^{-2at}}{\sqrt{{t-\frac{1}{t}}}} dt = \sqrt{\frac{a}{\pi}}\,\mathrm{K}_{\frac34}(a) \,\mathrm{K}_{\frac14}(a)$

Confusion regarding indefinite integral

Double Limits When Defining Improper Integral

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