Question: 1. Consider the solid E = {(x, y, z)| x + y+z 2z} with the density function f(x, y, z) = x + y

1. Consider the solid E = {(x, y, z)| x + y+z 2z} with the density function f(x, y, z) = x + y + z. (a) Use spherical coordinates to find the total volume of E. (b) Use spherical coordinates to find the total mass of E. (c) Find the average density over E. 2. Let W be the region within the cylinder x + y = 2 between the xy-plane and the cone z = Set up the iterated integral of f(x, y) = x + y over W using... (a) ...rectangular coordinates. (b) ...cylindrical coordinates. (c) ...spherical coordinates. Evaluate one of the three integrals (your choice!). x + y.

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