BC Calc III
Sample Polar Quiz
Name:
Calculator allowed.
You must show enough work so that I can recreate your results.
#1. Set up an integral or integrals that give the area of the region that is inside the inner
loop of the graph of r  1  2cos .
#2. Set up an integral or integrals that give the area inside one of the petals of
r  4cos 2 but outside of the circle r  2 .
#3.
a. Shade the region that represents the intersection of the regions enclosed by the
graphs of r  1  cos and r  4cos , then set up (but do not evaluate)
integral(s) to find the area of this region.
b. Find the equation of the tangent line (in Cartesian coordinates) to
r  1  cos at the point where the two graphs intersect.