8. Suppose that a solid E lies within the cylinder 2:2 + y2 = 1, below the plane 2: = 4 and above the paraboloid z = 1 3:2 yg. Suppose that the density is proportional to the distance from the z axis. Set up, but do not evaluate the integral for the mass of the solid. 9. Suppose that (p, 6, 925) are Spherical coordinates. (a) Sketch the region 0 S (25 S 9230, 0 g p g r, 09327rf0r50=7r/4andr=2. (b) Give the expressiOn for dV in spherical coordinates in terms of dab, tip and (if) (no justification required). (c) Set up, but do not evaluate the integral for the volume of the region in (a). (d) Evaluate the integral in (c). 10. Consider the integral / / (m+y)/(:ry) (M where T is the Trapezoid with vertices (1, 0), (2, 0), (0, 72), (0, i 1). . . T (a) Find the image S of the Trapezoid T under the change of variables it = a: +3}, 1) = :r y. Sketch S in the (um) plane. (b) Compute the J acobian for the change of variables a = a: + y, 1: = a: y. (Hint: expressing a: and y in terms of u and v is helpful). Convert the integral to an iterated integral in the (u, v) coordinates. (c) Set up but do not evaluate the integral as an iterated integral