The discussion focuses on evaluating the double integral of the function (xy + e^z) over the surface defined by the triangle with vertices (0,0,3), (1,0,2), and (0,4,1). The equation of the plane representing the triangle is established as z = 3 - x - (1/2)y. Participants emphasize the importance of projecting the vertices onto the xy-plane to determine the appropriate integration bounds for the double integral.
PREREQUISITESStudents and educators in multivariable calculus, mathematicians working with surface integrals, and anyone seeking to deepen their understanding of integration over complex geometric shapes.
PsychonautQQ said: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?