Math Solutions

[Step-by-Step] In the following integral ∫_Omega f(x, y) d x d y change the coordinate to polar coordinates x=r cos (φ), y=r sin (φ) and put

Question: In the following integral

\[\int_{\Omega} f(x, y) d x d y\]

change the coordinate to polar coordinates \(x=r \cos (\phi), y=r \sin (\phi)\) and put the order of integration if :

  1. \[\Omega=\left\{(x, y) \mid x^{2}+y^{2} \leq a^{2}\right\}\]
  2. \[\Omega=\left\{(x, y) \mid b^{2} \leq x^{2}+y^{2} \leq a^{2}\right\}\]
\[\Omega=\{(x, y) \mid 0 \leq x \leq 1,0 \leq y \leq 1-x\}\]

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