13.7#9

I can't quite understand how to do this problem. I've tried  |(7,0) | (7,0) | (8-z^2,0) z dy dz dx

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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.