how was the gaussian distribution developed? (question of an answer already done)

Question

I was looking for an answer for this question, I found it here on math stackexchage, but there's something in the answer I did not understand. I tried to add a comment too the answer, but I couldn't, because I dont have reputation enough. I cannot see where that tanget came from:

$ \int \int_{\mathbb{R}}f(x,y)dxdy = 2\pi \int_{0}^{\infty}tg(t)dt = \frac{2\pi}{B^2} $

link of the answer below: https://math.stackexchange.com/a/385427/755029

Could you help me, please?

Answer 1

There's no tangent there. The abbreviation for the tangent is $\tan$, not $\operatorname{tg}$; also, when a user has a reputation of several thousand, it’s rather likely that they can properly typeset math and wouldn’t italicize a function name.

The integrand is $t\cdot g(t)$. The factor $t$ is the Jacobian for the transformation from Cartesian to polar coordinates.