For full credit indicate clearly how you reached your answer. Each problem is worth 3 points.

1. A team of biologists is attempting to understand the dung beetle population in a large region. They determine that the population density is roughly given by the function 30000+2000x-1200y dung beetles paer square mile in a region ranging from 0 to 10 on their x axis and 0 to 15 on their y axis. According to their model, what is the total population of dung beetles in the research area?
 
 

2. Find the total volume between the function  and the xy-plane.
 
 

3. Find the volume of the region under the surface f(x,y) = 9 - (x + y)² in the first octant.
 
 

4. Find the average value of the function T(x,y) = 100/(1+x²+2y²) on the region in the first quadrant within which the value of T is at least 20.
 
 

5. Find the volume of the region between the surfaces z = x² - 2 and z = 2 - y².