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What is the recommended way in Mathematica to perform calculus integration range transformation?

Posted 6 months ago

Hi;

It is my understanding that Mathematica can perform calculus integration range coordinate transformation from, for example, from Cartesion to Polar or Cartesion to Cylindrical or Cartesion to Spherical or any other variation. However, I am having difficulty understanding exactly how to perform this transformation. Please review my attached notebook and help me understand what I am doing incorrectly.

Thanks,
Mitch Sandlin

POSTED BY: Mitchell Sandlin

I would try IntegrateChangeVariables:

Inactive[Integrate][f[x, y],
 {x, 0, 1},
 {y, -Sqrt[1 - x^2], Sqrt[1 - x^2]},
 {z, Sqrt[x^2 + y^2], 1}]
IntegrateChangeVariables[%,
 {r, theta, u}, "Cartesian" -> "Cylindrical"]
POSTED BY: Gianluca Gorni
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