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

score 30 · Answer 1 · 2026-04-13 08:24:12

30

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

Published on 13 Apr 2026 - 8:24

score 54 · Answer 2 · 2026-04-13 09:02:40

54

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

Published on 13 Apr 2026 - 9:02

score 96 · Answer 3 · 2026-04-16 02:20:32

96

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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 16 Apr 2026 - 2:20

score 115 · Answer 4 · 2026-04-14 20:44:17

115

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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 14 Apr 2026 - 20:44

score 216 · Answer 5 · 2026-04-16 02:48:16

216

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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 16 Apr 2026 - 2:48

score 126 · Answer 6 · 2026-04-16 03:06:13

126

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

Published on 16 Apr 2026 - 3:06

score 1.1k · Answer 7 · 2026-05-07 08:11:01

1.1k

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Cauchy Principal Value and Divergent Integrals

Published on 07 May 2026 - 8:11

score 318 · Answer 8 · 2026-04-15 22:05:34

318

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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 15 Apr 2026 - 22:05

score 747 · Answer 9 · 2026-04-09 10:09:42

747

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We square an integral, but why change a variable?

Published on 09 Apr 2026 - 10:09

score 58 · Answer 10 · 2026-04-08 19:35:44

58

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Finding the derivative of an integral function

Published on 08 Apr 2026 - 19:35

score 271 · Answer 11 · 2026-04-12 09:54:42

271

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Improper Integral Convergence involving $e^{x}$

Published on 12 Apr 2026 - 9:54

score 236 · Answer 12 · 2026-04-11 06:19:58

236

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Integral with delta distribution kernel at singularity

Published on 11 Apr 2026 - 6:19

score 39 · Answer 13 · 2026-04-12 11:19:33

39

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Convergence/Divergence of an Integral

Published on 12 Apr 2026 - 11:19

score 112 · Answer 14 · 2026-04-16 06:49:56

112

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

Published on 16 Apr 2026 - 6:49

score 112 · Answer 15 · 2026-04-16 02:16:18

112

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

Published on 16 Apr 2026 - 2:16

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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