Here $R$ is the unit circle. My question is in the second step can we substitute 1 for $x^2+y^2$ instead of $r^2$. In this case the answer will be $3\pi$. Which is correct $3\pi$ or ${3\pi}/2$?
2026-04-01 04:09:45.1775016585
Cartesian to Polar Coordinates Confusion
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You are integrating the area inside the unit circle, so the unit disk.
$$x² + y² = r² \neq 1$$
$$ 0 \leq x² + y² \leq 1$$
The answer is $3 \pi /2$.