SBC Calc III
No Calculator allowed.
Polar Problems
#1. Sketch the graph of r  4sin(2 ) (neatness and accuracy count), then set up an
integral or integrals that give the area inside one of the petals of r  4sin(2 ) .
#2. Find the (Cartesian) equation of the line tangent to the graph of r  1  2cos at
 3 
(r ,  )  1,  , then sketch this line on the graph below.
 2 
#3.
Shade the region that is inside the graph of r  1  cos and outside the graph of
r  3cos , then set up (but do not evaluate) integral(s) to find the area of this
region.
#4a. Sketch the graphs of r  2 and r  2 cos( ) together on the axes below. Neatness
and accuracy count!
b. Label all points of intersection on the graph above using polar coordinates.
c. Set up an expression involving one or more integrals that represents the area of the
region inside both the graphs of r  2 and r  2 cos( ) .
#5. Let R be the region in the second quadrant bounded by the graph of r  1  cos( ) . Set
up an integral or integrals that give the volume of the solid generated when the
region R is rotated about the y –axis.