*****************************
First of all, that double integral means you need to do a double integral, but you're doing a triple integral. That's your first clue. The fact that you have a double integral but the three variable function f(x,y,z) contributes to the misunderstanding but, second, that little "S" down under the double integral means that you are integrating over a surface just like we've been discussing the last two lectures. So now your job becomes figuring out the parameterization of the surface. The fact that x and z have the constraints 0≤x≤7, and 0≤z≤7 suggests that they should be equal parameters call them t,s, i.e. x=t and z=s. Then, since y=8-z^2 constrains y, you get the parameterization r(t,s) = < t, 8-s^2, s> . Now have at it.
