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# Using the Disk[] Primitive in Integration

Posted 15 days ago
 Hi; I am having difficulty using the Disk[] primitive to define my integration region - see attached. This method is quite new to me, however it seems really elegant, and I would sure like to learn how to use it correctly. Thanks,Mitch Sandlin
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Posted 14 days ago
 You can try IntegrateChangeVariables: IntegrateChangeVariables[ Inactive[Integrate][Cos[Sqrt[x^2 + y^2]], Element[{x, y}, Disk[]]], {r, \[Theta]}, "Cartesian" -> "Polar"] 
Posted 15 days ago
 I'm not sure how mathematically rigorous this is, but it seems to me that if you want to change the coordinate system, then you need to change the region: Integrate[Cos[r] r, {r, t} \[Element] Rectangle[{0, 0}, {1, 2 Pi}]] 
Posted 15 days ago
 All the examples I can find for using region-like primitives as integration regions use Cartesian coordinates rather than polar. So your integral would be written In[95]:= Integrate[Cos[Sqrt[x^2 + y^2]] , {x, y} \[Element] Disk[{0, 0}, 1]] Out[95]= 2 \[Pi] (-1 + Cos[1] + Sin[1])