Question

principal value of improper integrals

score 350 · Answer 1 · 2026-03-25 22:08:58

350

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principal value of improper integrals

Published on 25 Mar 2026 - 22:08

score 836 · Answer 2 · 2026-04-17 09:21:23

836

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If f is continuous and 0 < f(x) < g(x) on the interval [0, ∞) and $\int_0^\infty g(x) dx = M < \infty$ then $\int_0^\infty f(x) dx$ exists?

Published on 17 Apr 2026 - 9:21

score 100 · Answer 3 · 2026-04-16 23:56:03

100

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If $\int_1^\infty x^{-p} dx\,$ exists, then does $\int_1^\infty x^{-q} dx\,$ exist, where $q > p$?

Published on 16 Apr 2026 - 23:56

score 224 · Answer 4 · 2026-04-12 02:43:39

224

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Integral $\int_0^{\infty} \frac{\sin^2(x)}{x^2(x^2+1)} dx$ using Feynman method.

Published on 12 Apr 2026 - 2:43

score 30 · Answer 5 · 2026-04-11 10:38:52

30

Views

Improper integration limits

Published on 11 Apr 2026 - 10:38

score 254 · Answer 6 · 2026-04-09 15:54:06

254

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Improper integral substitution hint

Published on 09 Apr 2026 - 15:54

score 395 · Answer 7 · 2026-04-17 02:00:35

395

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Investigate absolute convergence of the integral $\int_0^\infty x^2\cos e^x\,dx$

Published on 17 Apr 2026 - 2:00

score 108 · Answer 8 · 2026-04-15 19:57:02

108

Views

To examine the convergence of the improper integrals

Published on 15 Apr 2026 - 19:57

score 879 · Answer 9 · 2026-04-10 01:56:37

879

Views

how do I find integrals where one limit tends to infinity?

Published on 10 Apr 2026 - 1:56

score 62 · Answer 10 · 2026-04-17 09:31:55

62

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About the convergence of the improper integrals $\int_0^{\pi/2} \frac{1}{e^x - \cos x} dx$, $\int_0^{\pi} \frac{1}{\cos \alpha - \cos x} dx$

Published on 17 Apr 2026 - 9:31

score 575 · Answer 11 · 2026-04-17 00:34:08

575

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Proving $\int_0^{\infty} \frac {x^{m-1} - x^{n-1}}{1-x} dx$ and $\int_0^{\infty} x^m (\log x)^m dx$

Published on 17 Apr 2026 - 0:34

score 872 · Answer 12 · 2026-04-17 04:53:13

872

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To test the convergence of $\int_0^{1} \frac{x^p \log x}{1+ x^2} dx$

Published on 17 Apr 2026 - 4:53

score 52 · Answer 13 · 2026-04-10 12:19:23

52

Views

Determing why the Integral comparison test cannot be used

Published on 10 Apr 2026 - 12:19

score 60 · Answer 14 · 2026-04-16 20:27:31

60

Views

$\int_0^1\frac{1}{r}\frac{1}{\left[\log\left(1+\frac{1}{r}\right)\right]^n}dr$ finite?

Published on 16 Apr 2026 - 20:27

score 27 · Answer 15 · 2026-04-14 06:13:30

27

Views

Divergence of a sequence involving logarithmic integrals

Published on 14 Apr 2026 - 6:13

List Question

principal value of improper integrals

If f is continuous and 0 < f(x) < g(x) on the interval [0, ∞) and $\int_0^\infty g(x) dx = M < \infty$ then $\int_0^\infty f(x) dx$ exists?

If $\int_1^\infty x^{-p} dx\,$ exists, then does $\int_1^\infty x^{-q} dx\,$ exist, where $q > p$?

Integral $\int_0^{\infty} \frac{\sin^2(x)}{x^2(x^2+1)} dx$ using Feynman method.

Improper integration limits

Improper integral substitution hint

Investigate absolute convergence of the integral $\int_0^\infty x^2\cos e^x\,dx$

To examine the convergence of the improper integrals

how do I find integrals where one limit tends to infinity?

About the convergence of the improper integrals $\int_0^{\pi/2} \frac{1}{e^x - \cos x} dx$, $\int_0^{\pi} \frac{1}{\cos \alpha - \cos x} dx$

Proving $\int_0^{\infty} \frac {x^{m-1} - x^{n-1}}{1-x} dx$ and $\int_0^{\infty} x^m (\log x)^m dx$

To test the convergence of $\int_0^{1} \frac{x^p \log x}{1+ x^2} dx$

Determing why the Integral comparison test cannot be used

$\int_0^1\frac{1}{r}\frac{1}{\left[\log\left(1+\frac{1}{r}\right)\right]^n}dr$ finite?

Divergence of a sequence involving logarithmic integrals

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