craincrew1015 craincrew1015

21-11-2017
Mathematics

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Evaluate xe^(x^2+y^2+z^2) where e is the portion of the unit ball x^2+y^2+z^2 < 1 that lies in the firat octant

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nobillionaireNobley nobillionaireNobley

01-12-2017

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]

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