Solutions to Stewart Section 13.7:3-19 odd

This gives one particular way of setting up the integrals. Of course other orders are possible, but in most cases these are the easiest or most natural.

7. 

9. 

11. 

13. Use the symmetry and homogeneity of the region to look only at the front left half (viewed from the usual perspective) and double that, producing .

15. It's an ugly problem, but if forced to do it here's what I'd do: First pull a trick, and interchange the x and z axes, so we're finding the integral of the function z for the region E bounded by z = 4x2 + 4y2 and the plane z = 4. Yes, you can do that. Then the integral sets up most easily in polar (or cylindrical, to be proper) coordinates as .

17. It's a tetrahedron with intercepts (6,0,0), (0,4,0), and (0,0,2). The most natural integral is .

19. .