[Re-closed as duplicate about Cartesian to Polar change of variables. See comment below.]

I propose that we should reopen this question question, and posted my reason in the comments.

It was closed as an exact duplicate of a thread asking how to evaluate a Gaussian integral. But actually, the question was why, when one converts from Cartesian to polar coordinates, $dx\,dy$ gets replaced by $r\,dr\,d\theta$. That's not what the other question was about. There are other ways to evaluate the Gaussian integral than by polar coordinates, and those other ways would be appropriate answers to that older question, but not to this one. In some ways, the presence of a Gaussian integral in this question is incidental. It was really only the particular occasion for the question about polar coordinates.

[Re-closed as duplicate about Cartesian to Polar change of variables. See comment below.]

I propose that we should reopen this question question, and posted my reason in the comments.

It was closed as an exact duplicate of a thread asking how to evaluate a Gaussian integral. But actually, the question was why, when one converts from Cartesian to polar coordinates, $dx\,dy$ gets replaced by $r\,dr\,d\theta$. That's not what the other question was about. There are other ways to evaluate the Gaussian integral than by polar coordinates, and those other ways would be appropriate answers to that older question, but not to this one. In some ways, the presence of a Gaussian integral in this question is incidental. It was really only the particular occasion for the question about polar coordinates.

I propose that we should reopen this question question, and posted my reason in the comments.

It was closed as an exact duplicate of a thread asking how to evaluate a Gaussian integral. But actually, the question was why, when one converts from Cartesian to polar coordinates, $dx\,dy$ gets replaced by $r\,dr\,d\theta$. That's not what the other question was about. There are other ways to evaluate the Gaussian integral than by polar coordinates, and those other ways would be appropriate answers to that older question, but not to this one. In some ways, the presence of a Gaussian integral in this question is incidental. It was really only the particular occasion for the question about polar coordinates.

[Re-closed as duplicate about Cartesian to Polar change of variables. See comment below.]

I propose that we should reopen this question question, and posted my reason in the comments.

It was closed as an exact duplicate of a thread asking how to evaluate a Gaussian integral. But actually, the question was why, when one converts from Cartesian to polar coordinates, $dx\,dy$ gets replaced by $r\,dr\,d\theta$. That's not what the other question was about. There are other ways to evaluate the Gaussian integral than by polar coordinates, and those other ways would be appropriate answers to that older question, but not to this one. In some ways, the presence of a Gaussian integral in this question is incidental. It was really only the particular occasion for the question about polar coordinates.