Find the region E for which the triple integral
int int int E(1-x^(2)-2y^(2)-3z^(2))dV
Is a maximum.

1 Answers

Best Answer

Remember that:
The points inside the ellipsoid x^(2)+2y^(2)+3z^(2)=1 satisfy the I not = uality
x^(2)+2y^(2)+3z^(2)<= 1
That means the expression 1-x^(2)-2y^(2)-3z^(2) is positive only when the point (x,y,z) is inside an ellipsoid.
Hence the maximum value of the Integral
int int int_(E)(1-x^(2)-2y^(2)-3z^(2))dV
occurs when E is the region inside an ellipsoid.
Result:
E is the region inside the ellipsoid x^(2)+2y^(2)+3z^(2)=1