Question

Show that the improper integral $\int_1^\infty f(x) \ dx$ exists iff $\sum_1^\infty a_n$ converges.

score 1.1k · Answer 1 · 2014-04-30 01:02:20

1.1k

Views

Show that the improper integral $\int_1^\infty f(x) \ dx$ exists iff $\sum_1^\infty a_n$ converges.

Published on 30 Apr 2014 - 1:02

score 56 · Answer 2 · 2014-04-30 15:28:53

56

Views

Convergence of improper Integral $\lim_{x -> 0} x^{\mu+n}{{\log x}\over {1+x}}$

Published on 30 Apr 2014 - 15:28

score 316 · Answer 3 · 2014-04-30 20:21:25

316

Views

Determining the convergence of $\int_{1}^{2}\frac{1}{\sqrt{x}(2-x)}\, \mathrm{d}x$ in simple way.

Published on 30 Apr 2014 - 20:21

score 759 · Answer 4 · 2014-05-01 09:13:49

759

Views

Elegant proof of $\int_{-\infty}^{\infty} \frac{dx}{x^4 + a x^2 + b ^2} =\frac {\pi} {b \sqrt{2b+a}}$?

Published on 01 May 2014 - 9:13

score 3.1k · Answer 5 · 2014-05-01 11:26:51

3.1k

Views

Lobachevsky's Formula for Integrals

Published on 01 May 2014 - 11:26

score 584 · Answer 6 · 2014-05-01 18:23:32

584

Views

How to prove divergence of the integral $\int_{0}^{\infty}\frac{\sin(x)}{x^{2}}dx$

Published on 01 May 2014 - 18:23

score 88 · Answer 7 · 2014-05-01 18:50:02

88

Views

Prove that $\int_{0}^{\infty}\left|e^{-xt}\frac{1-\cos(x)}{x}\right|dx$ converges

Published on 01 May 2014 - 18:50

score 218 · Answer 8 · 2014-05-01 19:23:08

218

Views

Discuss the convergence of $\int_0^1x^n \left[\log({1\over x})\right]^m \, dx$

Published on 01 May 2014 - 19:23

score 828 · Answer 9 · 2014-05-02 12:30:40

828

Views

Hints on calculating the integral $\int_0^1\frac{x^{19}-1}{\ln x}\,dx$

Published on 02 May 2014 - 12:30

score 172 · Answer 10 · 2014-05-02 20:44:31

172

Views

Integration problem: $\int _ {-\infty} ^ {\infty} \frac {e^{-x^2}}{\sqrt{\pi}} e^x\ dx$

Published on 02 May 2014 - 20:44

score 540 · Answer 11 · 2026-03-25 18:49:34

540

Views

Definite integral $\int_{R_0}^{R}\frac{dr}{r^2\sqrt{\frac{R_0-R_S}{R_0^3}-\frac{1}{r^2}\left(1-\frac{R_{s}}{r}\right)}}$

Published on 25 Mar 2026 - 18:49

score 192 · Answer 12 · 2026-03-26 00:58:55

192

Views

Tricky Integral equation - where to start?

Published on 26 Mar 2026 - 0:58

score 41 · Answer 13 · 2014-05-04 11:24:42

41

Views

How to compute this integration?

Published on 04 May 2014 - 11:24

score 102 · Answer 14 · 2014-05-04 11:31:51

102

Views

A question about convergence of improper parametric integral

Published on 04 May 2014 - 11:31

score 3.8k · Answer 15 · 2014-05-04 16:28:54

3.8k

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Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$

Published on 04 May 2014 - 16:28

List Question

Show that the improper integral $\int_1^\infty f(x) \ dx$ exists iff $\sum_1^\infty a_n$ converges.

Convergence of improper Integral $\lim_{x -> 0} x^{\mu+n}{{\log x}\over {1+x}}$

Determining the convergence of $\int_{1}^{2}\frac{1}{\sqrt{x}(2-x)}\, \mathrm{d}x$ in simple way.

Elegant proof of $\int_{-\infty}^{\infty} \frac{dx}{x^4 + a x^2 + b ^2} =\frac {\pi} {b \sqrt{2b+a}}$?

Lobachevsky's Formula for Integrals

How to prove divergence of the integral $\int_{0}^{\infty}\frac{\sin(x)}{x^{2}}dx$

Prove that $\int_{0}^{\infty}\left|e^{-xt}\frac{1-\cos(x)}{x}\right|dx$ converges

Discuss the convergence of $\int_0^1x^n \left[\log({1\over x})\right]^m \, dx$

Hints on calculating the integral $\int_0^1\frac{x^{19}-1}{\ln x}\,dx$

Integration problem: $\int _ {-\infty} ^ {\infty} \frac {e^{-x^2}}{\sqrt{\pi}} e^x\ dx$

Definite integral $\int_{R_0}^{R}\frac{dr}{r^2\sqrt{\frac{R_0-R_S}{R_0^3}-\frac{1}{r^2}\left(1-\frac{R_{s}}{r}\right)}}$

Tricky Integral equation - where to start?

How to compute this integration?

A question about convergence of improper parametric integral

Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$

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