List questions from improper-integrals

Published on 17 Apr 2026 - 1:20

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Given $\int_{-\infty}^\infty f(x)dx=0,$ Prove/Disprove claims

Published on 17 Apr 2026 - 8:02

314

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Prove $\int_1^\infty \frac{f(x)}{x}$ diverges

Published on 13 Apr 2026 - 21:04

142

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How to find limit of $\lim_{N \to \infty} \int_{N}^{e^N} xe^{-x^{2017}}dx$

Published on 15 Apr 2026 - 12:03

576

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Find $\lim_{x\to 1}\int_{x}^{x^2}\frac{1}{\ln {t}}\mathrm dt$.

Published on 17 Apr 2026 - 0:40

70

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Analytical explanation of $\delta$ functions in Fourier transform

Published on 13 Apr 2026 - 19:25

217

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f is $C^1$ and decreasing then $\int_1^{\infty}f(x)\sin(x)dx$ converges.

Published on 16 Apr 2026 - 11:46

141

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improper integral and dominated convergence

Published on 16 Apr 2026 - 19:35

283

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Evaluate the improper integral $\int_{-\infty}^0 {e^x}\text{sin}\, xdx$

Published on 17 Apr 2026 - 1:24

136

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Prove $\int_0^\infty \frac{e^{\frac{-1}{x}}-1}{x^{\frac{2}{3}}}dx$ converges

Published on 16 Apr 2026 - 5:30

110

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Continuity under integral sign

Published on 14 Apr 2026 - 3:14

2k

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Integral $\int\cos (2nx)\,\log \sin(x)\; dx $

Published on 15 Apr 2026 - 19:02

101

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Prove $\int_{-\infty}^\infty\frac{dx}{(1+x^2/a)^n}$ converges

Published on 15 Apr 2026 - 18:56

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Improper integral of complex exponential

Published on 12 Apr 2026 - 14:13

67

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Fourier integral expression of an attenuated wave

Published on 13 Apr 2026 - 21:16

List Question

Divergence of $\int_{0}^{1/2}\frac{x^s-1}{-\log(x)}$

Given $\int_{-\infty}^\infty f(x)dx=0,$ Prove/Disprove claims

Prove $\int_1^\infty \frac{f(x)}{x}$ diverges

How to find limit of $\lim_{N \to \infty} \int_{N}^{e^N} xe^{-x^{2017}}dx$

Find $\lim_{x\to 1}\int_{x}^{x^2}\frac{1}{\ln {t}}\mathrm dt$.

Analytical explanation of $\delta$ functions in Fourier transform

f is $C^1$ and decreasing then $\int_1^{\infty}f(x)\sin(x)dx$ converges.

improper integral and dominated convergence

Evaluate the improper integral $\int_{-\infty}^0 {e^x}\text{sin}\, xdx$

Prove $\int_0^\infty \frac{e^{\frac{-1}{x}}-1}{x^{\frac{2}{3}}}dx$ converges

Continuity under integral sign

Integral $\int\cos (2nx)\,\log \sin(x)\; dx $

Prove $\int_{-\infty}^\infty\frac{dx}{(1+x^2/a)^n}$ converges

Improper integral of complex exponential

Fourier integral expression of an attenuated wave

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