Ahoy everyone! I am new to Gaussian Integrals and my teachers cannot help me out (because they don't get it). So I turn to the Internet for answers. I have very basic doubts and would really appreciate a clear explanation. 1) How do we explain $dxdy = r\cdot dr d\theta$? I am looking for either a simple and intuitive geometric interpretation and/or an algebraic proof which starts from the very basics. 2)While converting cartesian coordinates to polar, I believe the limits for '$r$' are the same as those of $x$ (and $y$) but how do we exactly decide the limits of theta? I would appreciate any help. Thanks.
2026-03-25 09:46:54.1774432014
Limits and Jacobian for Gaussian Integrals
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The limits of theta ($\theta$) are $0$ and $\infty$, i.e. one full circle. And you should look at the following: https://www.math24.net/double-integrals-polar-coordinates/
I hope this helps you.