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Question on whether an integral is finite or infinite using certain inequality

score 27 · Answer 1 · 2018-02-22 13:29:17

27

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Question on whether an integral is finite or infinite using certain inequality

Published on 22 Feb 2018 - 13:29

score 51 · Answer 2 · 2018-02-22 15:17:29

51

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Exercise: Prove the following improper integral goes to $\;0\;$ as $\;n\to \infty\;$

Published on 22 Feb 2018 - 15:17

score 93 · Answer 3 · 2018-02-22 17:51:31

93

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Example of a continuous function $f:(0,1) \rightarrow \mathbb{R}$ such that $\int_{1/n}^1 f \, dx = 0$ for all $n$ but $\int_0^1 f \, dx$ DNE?

Published on 22 Feb 2018 - 17:51

score 113 · Answer 4 · 2018-02-23 06:05:17

113

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How to determine if $ \int_0^1 \frac{(\ln x)^5}{\sqrt{ x}}\mathrm dx$ diverges or converges without calculating the integral itself

Published on 23 Feb 2018 - 6:05

score 213 · Answer 5 · 2018-02-23 23:30:40

213

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Closed form of the integral $\int_{0}^\infty \frac{\tan^{-1}{x} \tan^{-1}{\frac{x}{2}} \tan^{-1}{\frac{x}{3}}}{x^2+1} \, \text{d}x$

Published on 23 Feb 2018 - 23:30

score 123 · Answer 6 · 2018-02-24 10:19:16

123

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Show $\int_{0}^{\infty} \sin^2{[\pi(x+\frac{1}{x})]}\,\mathrm{d}x$ diverges.

Published on 24 Feb 2018 - 10:19

score 1.1k · Answer 7 · 2026-03-17 19:18:47

1.1k

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Cauchy Principal Value and Divergent Integrals

Published on 17 Mar 2026 - 19:18

score 315 · Answer 8 · 2018-02-26 18:44:18

315

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Show that $\int\limits_0^{\infty}\frac {dt}te^{\cos t}\sin\sin t=\frac {\pi}2(e-1)$

Published on 26 Feb 2018 - 18:44

score 744 · Answer 9 · 2018-02-26 20:04:17

744

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We square an integral, but why change a variable?

Published on 26 Feb 2018 - 20:04

score 55 · Answer 10 · 2018-02-28 00:14:24

55

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Finding the derivative of an integral function

Published on 28 Feb 2018 - 0:14

score 268 · Answer 11 · 2018-03-01 17:34:14

268

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Improper Integral Convergence involving $e^{x}$

Published on 01 Mar 2018 - 17:34

score 234 · Answer 12 · 2026-03-24 23:59:20

234

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Integral with delta distribution kernel at singularity

Published on 24 Mar 2026 - 23:59

score 36 · Answer 13 · 2018-03-01 21:14:32

36

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Convergence/Divergence of an Integral

Published on 01 Mar 2018 - 21:14

score 109 · Answer 14 · 2018-03-02 02:15:57

109

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Evaluating $\int_{-\infty}^\infty \sin(x)\cos(x)\ dx$

Published on 02 Mar 2018 - 2:15

score 109 · Answer 15 · 2018-03-02 03:35:25

109

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Evaluate $\int_0^\infty\sum_{n=0}^\infty\frac{(-1)^n}{(n!)^t}\,dt$

Published on 02 Mar 2018 - 3:35

List Question

Question on whether an integral is finite or infinite using certain inequality

Exercise: Prove the following improper integral goes to $\;0\;$ as $\;n\to \infty\;$

Example of a continuous function $f:(0,1) \rightarrow \mathbb{R}$ such that $\int_{1/n}^1 f \, dx = 0$ for all $n$ but $\int_0^1 f \, dx$ DNE?

How to determine if $ \int_0^1 \frac{(\ln x)^5}{\sqrt{ x}}\mathrm dx$ diverges or converges without calculating the integral itself

Closed form of the integral $\int_{0}^\infty \frac{\tan^{-1}{x} \tan^{-1}{\frac{x}{2}} \tan^{-1}{\frac{x}{3}}}{x^2+1} \, \text{d}x$

Show $\int_{0}^{\infty} \sin^2{[\pi(x+\frac{1}{x})]}\,\mathrm{d}x$ diverges.

Cauchy Principal Value and Divergent Integrals

Show that $\int\limits_0^{\infty}\frac {dt}te^{\cos t}\sin\sin t=\frac {\pi}2(e-1)$

We square an integral, but why change a variable?

Finding the derivative of an integral function

Improper Integral Convergence involving $e^{x}$

Integral with delta distribution kernel at singularity

Convergence/Divergence of an Integral

Evaluating $\int_{-\infty}^\infty \sin(x)\cos(x)\ dx$

Evaluate $\int_0^\infty\sum_{n=0}^\infty\frac{(-1)^n}{(n!)^t}\,dt$

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