Question

Convergence of improper integral and infinite series

score 782 · Answer 1 · 2018-03-29 11:38:57

782

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Convergence of improper integral and infinite series

Published on 29 Mar 2018 - 11:38

score 414 · Answer 2 · 2026-03-25 14:15:48

414

Views

Inverse of a characteristic function

Published on 25 Mar 2026 - 14:15

score 129 · Answer 3 · 2018-04-01 16:09:58

129

Views

Showing $\int_{-\infty}^{\infty}\frac {\mathrm d x} {1+x+x^2}=3 \int_0^\infty \frac {\mathrm d x} {1+x+x^2}$

Published on 01 Apr 2018 - 16:09

score 40 · Answer 4 · 2018-04-01 19:35:28

40

Views

Improper integral with two problem points

Published on 01 Apr 2018 - 19:35

score 141 · Answer 5 · 2018-04-02 01:10:45

141

Views

Evaluating $ \lim_{n\rightarrow\infty} \int_a^\infty \frac{n}{1+n^2x^2}dx$.

Published on 02 Apr 2018 - 1:10

score 109 · Answer 6 · 2018-04-02 13:59:44

109

Views

Convergence of an improper integral $\int_3^\infty \frac{\sin(x)}{x+2\cos(x)}dx$

Published on 02 Apr 2018 - 13:59

score 42 · Answer 7 · 2018-04-02 16:25:58

42

Views

If $\mu>1$, $\int_a^\infty f dx $ converges absolutely and if $\mu=1$ and $A\neq 0$,$\int_a^\infty f dx $ diverges

Published on 02 Apr 2018 - 16:25

score 146 · Answer 8 · 2026-03-25 15:42:12

146

Views

Evaluating $\int_{-\pi}^{\pi}\frac{1}{ai+b\cos(x)}dx$ for real $a,b$

Published on 25 Mar 2026 - 15:42

score 142 · Answer 9 · 2018-04-03 15:17:14

142

Views

How does $\iint_{\mathbf{ℝ^2}}\frac{x}{1+x^2+y^2}dxdy$ diverge?

Published on 03 Apr 2018 - 15:17

score 38 · Answer 10 · 2018-04-04 04:26:58

38

Views

Improper integral with derivative within integral

Published on 04 Apr 2018 - 4:26

score 74 · Answer 11 · 2018-04-04 09:08:31

74

Views

Want to solve $\int \frac{\sqrt{t}}{1-2t}dt$ by substitution using only $t = \frac{1}{2}\cos^2\theta$

Published on 04 Apr 2018 - 9:08

score 334 · Answer 12 · 2018-04-04 12:38:40

334

Views

How can I prove the Wolfram Alpha result $\int_0^{\infty} \frac{(\sin x)^2}{x^2-\pi ^2} dx=-\frac1{2\pi}$?

Published on 04 Apr 2018 - 12:38

score 24 · Answer 13 · 2018-04-04 12:39:36

24

Views

Checking the calculation of the improper integral

Published on 04 Apr 2018 - 12:39

score 165 · Answer 14 · 2026-03-25 17:37:36

165

Views

convergence of improper integral wrt comparison to improper integrals known to exist

Published on 25 Mar 2026 - 17:37

score 40 · Answer 15 · 2018-04-05 11:22:46

40

Views

Connection between summation and integration

Published on 05 Apr 2018 - 11:22

List Question

Convergence of improper integral and infinite series

Inverse of a characteristic function

Showing $\int_{-\infty}^{\infty}\frac {\mathrm d x} {1+x+x^2}=3 \int_0^\infty \frac {\mathrm d x} {1+x+x^2}$

Improper integral with two problem points

Evaluating $ \lim_{n\rightarrow\infty} \int_a^\infty \frac{n}{1+n^2x^2}dx$.

Convergence of an improper integral $\int_3^\infty \frac{\sin(x)}{x+2\cos(x)}dx$

If $\mu>1$, $\int_a^\infty f dx $ converges absolutely and if $\mu=1$ and $A\neq 0$,$\int_a^\infty f dx $ diverges

Evaluating $\int_{-\pi}^{\pi}\frac{1}{ai+b\cos(x)}dx$ for real $a,b$

How does $\iint_{\mathbf{ℝ^2}}\frac{x}{1+x^2+y^2}dxdy$ diverge?

Improper integral with derivative within integral

Want to solve $\int \frac{\sqrt{t}}{1-2t}dt$ by substitution using only $t = \frac{1}{2}\cos^2\theta$

How can I prove the Wolfram Alpha result $\int_0^{\infty} \frac{(\sin x)^2}{x^2-\pi ^2} dx=-\frac1{2\pi}$?

Checking the calculation of the improper integral

convergence of improper integral wrt comparison to improper integrals known to exist

Connection between summation and integration

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