Final answer:
To determine the surface integral of the function (x, y, z) = xy on a plane, rearrange the equation of the plane, substitute the expression for x into the function, and integrate the function over the plane.
Step-by-step explanation:
To determine the surface integral of the function (x, y, z) = xy on the plane of equation x + 2y + 4z = 8 for (x, y, z > 0), we need to define the surface and then calculate the integral.
First, we rearrange the equation x + 2y + 4z = 8 to isolate x and express it in terms of y and z: x = 8 - 2y - 4z.
Next, we substitute the expression for x into the function to get the function in terms of y and z: f(y, z) = (8 - 2y - 4z) * y.
Finally, we integrate the function f(y, z) over the given plane using appropriate bounds for y and z.