In[]:=
deploy
Sun 28 Aug 2022 10:09:51
In[]:=
results={};For[d=2,d<=11,d+=1,xvec=Array[x,d];center=ConstantArray[0,d];area=Integrate[1,xvec∈Sphere[center]];result=Integrate[Abs[x[1]],xvec∈Sphere[center]]/area;AppendTo[results,{d-1,result}];];
In[]:=
TableForm[results]
Out[]//TableForm=
1 | 2 π |
2 | 1 2 |
3 | 4 3π |
4 | 3 8 |
5 | 16 15π |
6 | 5 16 |
7 | 32 35π |
8 | 35 128 |
9 | 256 315π |
10 | 63 256 |