Extra credit Problem #6 (4 pts)
Use appropriate coordinates to find the average distance to the origin for points in the
ice cream cone region bounded by f  x , y  8  x 2  y 2 from above and
f  x , y  x 2  y 2 from below.
Extra credit Problem #7 (4 pts)
Use the change of variables u = xy and v = xy2 to compute
 xy
2
dA where R is the
R
region bounded by xy = 1, xy = 4, xy2 =1 and , xy2 =4.
Extra credit Problem #8 (4 pts)
A forest next to a road has a shape of a trapezoid given by the points (-2,5), (0,0), (6,0)
and (8,5) such that the longer side is by the road (units given in miles). The population
density of rabbits is proportional to the distance from the road. It is 0 at the road and 10
rabbits per square miles at the opposite edge of the forest. Find the total rabbit population
of the forest.
Remember:
population =
  ( x, y)dA
R
in the region R.
where (x,y) is the population density function