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