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Using the Disk[] Primitive in Integration

Posted 15 days ago


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.

Mitch Sandlin

POSTED BY: Mitchell Sandlin
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You can try IntegrateChangeVariables:

 Inactive[Integrate][Cos[Sqrt[x^2 + y^2]],
  Element[{x, y}, Disk[]]],
 {r, \[Theta]}, "Cartesian" -> "Polar"]
POSTED BY: Gianluca Gorni
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 BY: Eric Rimbey

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])
POSTED BY: Jason Biggs
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