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Integrating over a 3D ExampleData shape?

Posted 2 months ago
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Hi, I am a new student with Mathematica. I would like to ask something : there is an exercise we were doing in class and I did not understand well. Can I get help?

NIntegrate[ExampleData[{"Geometry3D", "Beethoven"}] 1, {x, y, z}]
Integrate[Sin[x], x]

How do I get the answer using this?
enter image description here

2 Replies
Posted 2 months ago

Or this which gives the same result, but disagrees with what is shown as the correct answer: 872.56

NIntegrate[1, {x, y, z} ∈ ExampleData[{"Geometry3D", "Beethoven"}, "Region"]]

Maybe something like this?

NIntegrate[1, Element[{x, y, z},
  DiscretizeGraphics@ExampleData[{"Geometry3D", "Beethoven"}]]]
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