Evaluate the surface of the integral rr s f(x, y, z)ds using an explicit representation of the surface f(x, y, z) = e z where z = 18 − 3x − 9y in the first octant. integrate with respect to x first.

The part of the plane in the first octant is one of the faces of a tetrahedron whose vertices correspond exactly to the intercepts of the plane. These are





We can parameterize this surface with the vector-valued function



where and . Then the surface element is



so the surface integral becomes

Atranslation 6 units to the right and 4 down