Question

Show that $I=\int_0^{\infty}e^{-a^2x^2}x^m\sin{nx}\,dx$ is absolutely converges for $m>0$

score 58 · Answer 1 · 2026-04-15 21:37:45

58

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Show that $I=\int_0^{\infty}e^{-a^2x^2}x^m\sin{nx}\,dx$ is absolutely converges for $m>0$

Published on 15 Apr 2026 - 21:37

score 308 · Answer 2 · 2026-04-29 12:50:27

308

Views

Integrating the Gaussian function over (nearly) symmetric bounds

Published on 29 Apr 2026 - 12:50

score 1.5k · Answer 3 · 2026-04-15 00:06:23

1.5k

Views

Uniform random variables: joint density function to compute product

Published on 15 Apr 2026 - 0:06

score 118 · Answer 4 · 2026-04-12 05:24:47

118

Views

Integral Identities

Published on 12 Apr 2026 - 5:24

score 71 · Answer 5 · 2026-04-12 12:31:53

71

Views

Evaluating an integral expression in $\mathbb{C}$

Published on 12 Apr 2026 - 12:31

score 73 · Answer 6 · 2026-04-11 00:44:54

73

Views

How am I supposed to approach this problem?

Published on 11 Apr 2026 - 0:44

score 120 · Answer 7 · 2026-03-25 03:19:43

120

Views

Evaluating $\int_{0}^{\frac{\pi}{2}}d\phi \frac{e^{-D \cos^2 \phi}}{A+B\tan^2 \phi}$

Published on 25 Mar 2026 - 3:19

score 83 · Answer 8 · 2026-04-16 13:05:50

83

Views

Find $\lim_{n \to \infty}(n - \frac{1}{2^n} \sum_{k=1}^{2^n}\log_{2}(k+2^{n-1}))$ using Riemann sums

Published on 16 Apr 2026 - 13:05

score 147 · Answer 9 · 2026-04-24 18:58:36

147

Views

Calculate $\lim _{x \to \infty} (\int_0^x e^{t^2} dt)^{2}(\int_0^x e^{2 t^2} dt)^{-1}$

Published on 24 Apr 2026 - 18:58

score 57 · Answer 10 · 2026-04-17 09:49:17

57

Views

Prove that $\int_{x}^{x+ (\ln x /x)} e^{t^2} dt > \frac{e^{x^2} \ln x}{2 x}$

Published on 17 Apr 2026 - 9:49

score 957 · Answer 11 · 2026-04-30 01:49:24

957

Views

Solid volume using double integral

Published on 30 Apr 2026 - 1:49

score 101 · Answer 12 · 2026-04-15 03:38:47

101

Views

Question on how to compute the volume of an n-simplex

Published on 15 Apr 2026 - 3:38

score 142 · Answer 13 · 2026-05-02 20:03:52

142

Views

Understanding the derivation of $\sum_{n\leq N}\frac{1}{n^\alpha} = \int_1^N\frac{1}{x^\alpha}d[x]+1.$

Published on 02 May 2026 - 20:03

score 109 · Answer 14 · 2026-04-12 07:55:39

109

Views

Integral of exponential with absolute exponent

Published on 12 Apr 2026 - 7:55

score 64 · Answer 15 · 2026-04-29 12:49:44

64

Views

Greens's formula with Hodge-*

Published on 29 Apr 2026 - 12:49

List Question

Show that $I=\int_0^{\infty}e^{-a^2x^2}x^m\sin{nx}\,dx$ is absolutely converges for $m>0$

Integrating the Gaussian function over (nearly) symmetric bounds

Uniform random variables: joint density function to compute product

Integral Identities

Evaluating an integral expression in $\mathbb{C}$

How am I supposed to approach this problem?

Evaluating $\int_{0}^{\frac{\pi}{2}}d\phi \frac{e^{-D \cos^2 \phi}}{A+B\tan^2 \phi}$

Find $\lim_{n \to \infty}(n - \frac{1}{2^n} \sum_{k=1}^{2^n}\log_{2}(k+2^{n-1}))$ using Riemann sums

Calculate $\lim _{x \to \infty} (\int_0^x e^{t^2} dt)^{2}(\int_0^x e^{2 t^2} dt)^{-1}$

Prove that $\int_{x}^{x+ (\ln x /x)} e^{t^2} dt > \frac{e^{x^2} \ln x}{2 x}$

Solid volume using double integral

Question on how to compute the volume of an n-simplex

Understanding the derivation of $\sum_{n\leq N}\frac{1}{n^\alpha} = \int_1^N\frac{1}{x^\alpha}d[x]+1.$

Integral of exponential with absolute exponent

Greens's formula with Hodge-*

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