If I were to evaluate
∫∫
Ω
cos
2
x
+
2
y
A
in polar coordinates with
Ω
being a disk centered at the origin with radius
1
, I would get the answer of:
In[]:=
Integrate[Cos[r]r,{θ,0,2π},{r,0,1}]
Out[]=
2π(-1+Cos[1]+Sin[1])
However, if I try using the primitive Disk[], I get :
In[]:=
Integrate[Cos[r]r,{θ,r}∈Region[Disk[{0,0},1]]]
Out[]=
0
Additionally, I tried using the statement without the Region[] function:
In[]:=
Integrate[Cos[r]r,{θ,r}∈Disk[{0,0},1]]
Out[]=
0