2 Jun
2015
2 Jun
'15
6:46 p.m.
In[1]:= num[x_,y_,z_] := (x y z - (1-x)(1-y)(1-z))^2 In[2]:= den(x_,y_,z_] := (1-x(1-z))(1-y(1-x))(1-z(1-y)) In[3]:= f[x_,y_,z_] := num[x,y,z]/den[x,y,z] In[4]:= NIntegrate[f[x,y,z],{x,0,1},{y,0,1},{z,0,1}] Out[4]= 0.130396 but: In[5]:= Integrate[f[x,y,z],{x,0,1},{y,0,1},{z,0,1}] Out[5]= 10 10 ??? Huh??? (Especially since the maximum value of f[x,y,z] over [0,1]^3 is f[0,0,0] = 1.) Rational explanations, if any, welcomed. ——Dan