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10.5 Area and Arc Length in Polar Coordinates 627
10.5 Area and Arc Length in Polar Coordinates
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Write an integral that represents the area of the shaded region for as shown
in the figure. Do not evaluate the integral.
a.
b.
c.
d.
e.
628 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 2. Find the area of the interior of .
a.
b.
c.
d.
e.
____ 3. Find the area of one petal of .
a.
b.
c.
d.
e.
____ 4. Find the area of the interior of .
a.
b.
c.
d.
e.
10.5 Area and Arc Length in Polar Coordinates 629
____ 5. Find the area of the inner loop of .
a.
b.
c.
d.
e.
____ 6. Find the area of the region lying between the loops of .
a.
b.
c.
d.
e.
630 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 7. Find all points of intersection of the graphs of the equations.
a.
b.
c.
d.
e.
____ 8. Find the points of intersection of the graphs of the equations.
a.
b.
c.
d.
e.
10.5 Area and Arc Length in Polar Coordinates 631
____ 9. Find the area of the common interior of the polar equations
by sketching the graph of the equations using the graphing utility.
a.
b.
c.
d.
e.
____ 10. Find the area of inside and outside by sketching the graph of the
equations using the graphing utility.
a.
b.
c.
d.
e.
____ 11. Find the length of the curve over the interval .
a.
b.
c.
d.
e.
632 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 12. Find the length of the curve over the given interval.
a.
b.
c.
d.
e.
____ 13. Find the length of the curve over the given interval.
a.
b.
c.
d.
e.
____ 14. Find the length of the curve over the given interval.
a.
b.
c.
d.
e.
____ 15. Find the length of the curve over the interval . Round your
answer to two decimal places.
a. 0.58
b. 3.46
c. 2.00
d. 1.15
e. 1.73
10.5 Area and Arc Length in Polar Coordinates 633
____ 16. Find the area of the surface formed by revolving about the polar axis the following
curve over the given interval.
a.
b.
c.
d.
e.
____ 17. Find the area of the surface formed by revolving about the axis the following
curve over the given interval.
a.
b.
c.
d.
e.
634 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
10.5 Area and Arc Length in Polar Coordinates
Answer Section
