Let E be the solid region that is inside the sphere x

2 + y

2 + z

2 = 2, on the left of the cone y = x

2 + z

2, on the

right of the XZ-plane and in the first octant. Let the density of the solid at (x, y, z) be (x, y, z) = x

2 + z

2.

(a). Sketch the solid region E. (6 points)

(b). Describe E (using the set builder notation), then set up, but DO NOT evaluate, iterated integral(s) for the mass

of E using the rectangular coordinates.

(c). Repeat (b) using the cylindrical coordinates.

(d). Repeat (b) using the spherical coordinates.

(e). Evaluate ONE of the set ups in (b), (c), and (d).