Question

How to compute the improper integral

score 84 · Answer 1 · 2026-04-11 07:58:12

84

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How to compute the improper integral

Published on 11 Apr 2026 - 7:58

score 159 · Answer 2 · 2026-04-17 05:22:57

159

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Prove $\int_0^1 \frac{\log x}{x^2} \cos x$ is convergent

Published on 17 Apr 2026 - 5:22

score 749 · Answer 3 · 2026-04-17 05:06:18

749

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Is $\int_0^{+\infty}\frac{\sin \ln x}{\sqrt x}\,dx$ convergent or absolutely convergent?

Published on 17 Apr 2026 - 5:06

score 80 · Answer 4 · 2026-04-24 21:32:09

80

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Showing that $\int_0^{\infty}f_n(x)e^{-x}dx \rightarrow \int_0^{\infty} f(x)e^{-x}dx \quad n \rightarrow \infty$ for a sequence $f_n$ of functions

Published on 24 Apr 2026 - 21:32

score 137 · Answer 5 · 2026-04-15 21:57:12

137

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Proof that $ \int_0^\infty \frac{(f'(x))^2}{f(x)^{1980}} dx < \infty$

Published on 15 Apr 2026 - 21:57

score 148 · Answer 6 · 2026-04-17 09:04:08

148

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Does the property $\int_{a}^b[ f(x) + g(x)] dx = \int_{a}^b f(x) dx + \int_{a}^b g(x) dx$ hold for improper integrals?

Published on 17 Apr 2026 - 9:04

score 44 · Answer 7 · 2026-04-15 17:23:39

44

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Justify $\frac{d}{ds} \int_{0}^{\infty} e^{-e^{is}\cdot x^2} dx$ = $ \int_{0}^{\infty} \frac{d}{ds} e^{-e^{is}\cdot x^2} dx$ for fresnel integral

Published on 15 Apr 2026 - 17:23

score 475 · Answer 8 · 2026-04-15 01:12:48

475

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If a function is Riemann integrable and Lebesgue integrable, the two integrals are the same?

Published on 15 Apr 2026 - 1:12

score 133 · Answer 9 · 2026-04-16 18:54:02

133

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Evaluate $\int_{-\infty}^{\infty}\sin(ax)\operatorname{sech}^4(b(x-c))dx$, for $a,b,c>0$

Published on 16 Apr 2026 - 18:54

score 57 · Answer 10 · 2026-04-17 14:34:02

57

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Prove or disprove. Improper integral

Published on 17 Apr 2026 - 14:34

score 963 · Answer 11 · 2026-04-15 20:38:41

963

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Convergence of $ I=\int_0^\infty \sin x\sin(x^2)\mathrm{d}x$

Published on 15 Apr 2026 - 20:38

score 1k · Answer 12 · 2026-04-12 03:48:12

1k

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Convergence of improper double integral.

Published on 12 Apr 2026 - 3:48

score 90 · Answer 13 · 2026-04-16 04:48:43

90

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Prove Uniform integrability of $ \int_{0}^{\infty} e^{-e^{is}\cdot x^2} dx $

Published on 16 Apr 2026 - 4:48

score 421 · Answer 14 · 2026-04-14 11:05:31

421

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Prove the following improper integral converges

Published on 14 Apr 2026 - 11:05

score 411 · Answer 15 · 2026-03-26 12:33:31

411

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Schwinger proper time representation of log x

Published on 26 Mar 2026 - 12:33

List Question

How to compute the improper integral

Prove $\int_0^1 \frac{\log x}{x^2} \cos x$ is convergent

Is $\int_0^{+\infty}\frac{\sin \ln x}{\sqrt x}\,dx$ convergent or absolutely convergent?

Showing that $\int_0^{\infty}f_n(x)e^{-x}dx \rightarrow \int_0^{\infty} f(x)e^{-x}dx \quad n \rightarrow \infty$ for a sequence $f_n$ of functions

Proof that $ \int_0^\infty \frac{(f'(x))^2}{f(x)^{1980}} dx < \infty$

Does the property $\int_{a}^b[ f(x) + g(x)] dx = \int_{a}^b f(x) dx + \int_{a}^b g(x) dx$ hold for improper integrals?

Justify $\frac{d}{ds} \int_{0}^{\infty} e^{-e^{is}\cdot x^2} dx$ = $ \int_{0}^{\infty} \frac{d}{ds} e^{-e^{is}\cdot x^2} dx$ for fresnel integral

If a function is Riemann integrable and Lebesgue integrable, the two integrals are the same?

Evaluate $\int_{-\infty}^{\infty}\sin(ax)\operatorname{sech}^4(b(x-c))dx$, for $a,b,c>0$

Prove or disprove. Improper integral

Convergence of $ I=\int_0^\infty \sin x\sin(x^2)\mathrm{d}x$

Convergence of improper double integral.

Prove Uniform integrability of $ \int_{0}^{\infty} e^{-e^{is}\cdot x^2} dx $

Prove the following improper integral converges

Schwinger proper time representation of log x

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