Mathematics

Brooklynn

30 March, 09:46

This problem asks you to investigate the average value of some different quantities.

(a) Set up, but do not evaluate, an iterated integral expression whose value is the average sum of all real numbers a, y, and z that have the following property: y is between 0 and 2, z is greater than or equal to 0 but cannot exceed 2y, and z is greater than or equal to 0 but cannot exceed z + y

(b) Set up, but do not evaluate, an integral expression whose value represents the average value of f (, y, z) + y+z over the solid region in the first octant bounded by the sultneo e a and the rd platesiom in th - by the surface z = 4-x-v2 and the coordinate planes x = 0, y = 0, z = 0.

(c) How are the quantities in (a) and (b) similar? How are they different?