6 pts
BC Calc III
No Calculator allowed.
Quiz #7 Name:
You must show enough work so that I can recreate your results.
#1. Sketch the graph of r

4 sin(2 ) ( neatness and accuracy count), then set up an integral or integrals that give the area inside one of the petals of r

4 sin(2 ) .
5 pts #2. Find the (Cartesian) equation of the line tangent to the graph of r 1 2cos



1,
3

, then sketch this line on the graph below.
2
at

6 pts #3. Shade the region that is inside the graph of r 1 cos r

3cos


and outside the graph of
, then set up (but do not evaluate) integral(s) to find the area of this region.

4 pts
#4a. Sketch the graphs of r

2 and r
  and accuracy count!
together on the axes below. Neatness
2 pts
4 pts 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 pts #5. Let R be the region in the second quadrant bounded by the graph of r
   up an integral or integrals that give the volume of the solid generated when the region R is rotated about the y –axis.
. Set