1) Set up triple integral expressions in cylindrical coordinates, and then in spherical coordinates, to find the volume for each solid. No integration required. Parts a) and b) are two separate problems, each to be done in the two coordinate systems (four different triple integral expressions to set up.) 6. (15 pts) Sketch the region of integration for the following double integral, and compute the integral: ∫ 9 0 ∫ 3 √ y 3ex 3 dx dy. Ans: We first see that it is impossible to integrate the iterated integral as set up (ex 3 has no elementary antiderivative with respect to x). The region of integration is 0 ≤ y ≤ 9,√ y ≤ x ≤ 3.