Surface Integral Homework: Double Integral of (xy+e^z)dS

[PsychonautQQ]

Homework Statement

Take the double Integral of (xy+e^z)dS where S is the triangle with vertices (0,0,3),(1,0,2),(0,4,1).

Homework Equations

The Attempt at a Solution

So the equation of the plane for the triangle given is z = 3 - x - (1/2)y. We plugged that Z into the z from the function given and are having a bit of trouble finding the bounds we integrate the double integral over. Help?

 

[LCKurtz]

Homework Statement

Take the double Integral of (xy+e^z)dS where S is the triangle with vertices (0,0,3),(1,0,2),(0,4,1).

Homework Equations

The Attempt at a Solution

So the equation of the plane for the triangle given is z = 3 - x - (1/2)y. We plugged that Z into the z from the function given and are having a bit of trouble finding the bounds we integrate the double integral over. Help?

If you take z as a function of x and y, you want to project the 3 vertices down to the xy plane and use the triangle it forms for the limits.