Integrating over a 3D ExampleData shape?

[t02su21 (Salmon UULENGA)]

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?

[gianlucagorni]

Maybe something like this?

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

[rohitnamjoshi]

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"]]