In[]:=
fxy=Exp[-1*(((x-ux)/sx)^2+((y-uy)/sy)^2-2r((x-ux)*(y-uy)/(sx*sy)))/(2(1-r^2))]/(2*Pi*sx*sy*(1-r^2)^0.5)​​fy=(1/(sy(2*Pi)^0.5))*Exp[-(1/2)*((y-uy)/sy)^2]​​f=x^2*y*(fxy/fy)​​Integrate[f,{x,-Infinity,Infinity},{y,-Infinity,Infinity}]​​
Out[]=
-
2
(-ux+x)
2
sx
-
2r(-ux+x)(-uy+y)
sxsy
+
2
(-uy+y)
2
sy
2(1-
2
r
)

2π
0.5
(1-
2
r
)
sxsy
Out[]=
0.398942
-
2
(-uy+y)
2
2
sy

sy
Out[]=
0.398942
2
(-uy+y)
2
2
sy
-
2
(-ux+x)
2
sx
-
2r(-ux+x)(-uy+y)
sxsy
+
2
(-uy+y)
2
sy
2(1-
2
r
)

2
x
y
0.5
(1-
2
r
)
sx
Cloud
::timelimit
:This computation has exceeded the time limit for your plan.
​
Out[]=
$Aborted
In[]:=
​
In[]:=
Integrate[Sin[x],{x,0,Pi/2}]
Out[]=
1