Question

Calculate $f'(\sqrt{\pi})+g'(\sqrt{\pi})$ of the integrals $f(x)=(\int_{0}^{x}e^{-t^2}dt)^2$ and $g(x)=\int_{0}^{1}\frac{e^{-x^2(1+t^2)}}{1+t^2}dt$

score 249 · Answer 1 · 2016-07-06 02:49:13

249

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Calculate $f'(\sqrt{\pi})+g'(\sqrt{\pi})$ of the integrals $f(x)=(\int_{0}^{x}e^{-t^2}dt)^2$ and $g(x)=\int_{0}^{1}\frac{e^{-x^2(1+t^2)}}{1+t^2}dt$

Published on 06 Jul 2016 - 2:49

score 103 · Answer 2 · 2016-07-17 02:41:15

103

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Prove $ \int_{-\infty}^{\infty} e^{-\alpha(x-c)^2} x^{2n} dx =\int_{-\infty}^{\infty} e^{-\alpha x^2} x^{2n} dx$

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559

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125

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943

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score 659 · Answer 6 · 2016-08-04 23:14:21

659

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97

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score 25 · Answer 8 · 2016-08-25 23:31:01

25

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score 458 · Answer 9 · 2016-08-30 14:19:47

458

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score 44 · Answer 10 · 2016-09-04 20:19:11

44

Views

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83

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456

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score 757 · Answer 13 · 2016-09-12 22:27:48

757

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score 588 · Answer 14 · 2016-09-18 14:04:19

588

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Published on 18 Sep 2016 - 14:04

score 362 · Answer 15 · 2016-09-23 21:40:49

362

Views

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List Question

Calculate $f'(\sqrt{\pi})+g'(\sqrt{\pi})$ of the integrals $f(x)=(\int_{0}^{x}e^{-t^2}dt)^2$ and $g(x)=\int_{0}^{1}\frac{e^{-x^2(1+t^2)}}{1+t^2}dt$

Prove $ \int_{-\infty}^{\infty} e^{-\alpha(x-c)^2} x^{2n} dx =\int_{-\infty}^{\infty} e^{-\alpha x^2} x^{2n} dx$

Path length of Gaussian

Does Gaussian convolution respects order?

Multidimensional Gaussian integrals with a complex quadratic term

integrate product of two gaussian pdfs where one marginal is not gaussian

Gaussian Integration

Where was my reasoning off in evaluating the expectation value of $x$ in this Gaussian distribution?

Why this kind transformation of Gauss-Hermite quadrature is wrong?

$X$ is a Gaussian random variable with $\nu_x=0$ and $\sigma_X$. Plot $P(X>1)$ as a function of $\sigma_X$

Method of stationary phase, with Laplacian eigenvalue exponent

Integral of Gaussian PDF

Multivariate Gaussian: How to show $\Sigma$ is covariance matrix?

Questions on the integration $\int_0^\infty e^{-(x^2+a^2/x^2)}dx$

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