Given
[tex]\int\int\int_E xe^{(x^2+y^2+z^2)}[/tex]
where E is the portion of the unit ball [tex]x^2+y^2+z^2\leq1[/tex] that lies in the first octant.
This can be evaluated as follows:
[tex]\int_0^1\int_0^{\sqrt{1-x^2}}\int_0^{\sqrt{1-x^2-y^2}} xe^{(x^2+y^2+z^2)}dzdydx=0.392699[/tex]
