15.4 Green’s Theorem 927
15.4 Green’s Theorem
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Verify Green’s Theorem by evaluating both integrals
for the path C defined as the boundary of the region
lying between the graphs of and .
a.
b.
c.
d.
e.
____ 2. Verify Green’s Theorem by setting up and evaluating both integrals
for the path C: square with vertices (0,0), (10,0), (10,10), (0,10).
a.
b.
928 Chapter 15: Vector Analysis
c.
d.
e.
____ 3. Use Green’s Theorem to evaluate the integral
for the path C: boundary of the region lying between the graphs of y = x and y = .
a.
b.
c.
d.
e.
15.4 Green’s Theorem 929
____ 4. Use Green’s Theorem to evaluate the integral for the path
C defined as .
a.
b.
c.
d.
e.
____ 5. Use Green’s Theorem to evaluate the integral where C is
the boundary of the region lying inside the rectangle bounded by and
outside the square bounded by .
a.
b.
c.
d.
e.
____ 6. Use Green’s Theorem to evaluate the integral
for the path C: boundary of the region lying between the graphs of and .
a.
b.
c.
d.
e.
930 Chapter 15: Vector Analysis
____ 7. Use Green’s Theorem to evaluate the integral
for the path C: .
a.
b.
c.
d.
e.
____ 8. Use Green’s Theorem to evaluate the line integral
where C is .
a.
b.
c.
d.
e.
____ 9. Use Green’s Theorem to evaluate the line integral
where C is the boundary of the region lying between the graphs
of the circle and the ellipse .
a.
b.
c.
d.
e.
____ 10. Use Green’s Theorem to calculate the work done by the force on a particle that is
moving counterclockwise around the closed path C.
a.
b.
c.
d.
e.
15.4 Green’s Theorem 931
____ 11. Use Green’s Theorem to calculate the work done by the force
on a particle that is moving counterclockwise around the closed path
C where C is the boundary of the region lying between the graphs of . Round
your answer to two decimal places.
a.
b.
c.
d.
e.
____ 12. Set up and evaluate a line integral to find the area of the region R bounded by the
graph of .
a. where
b. where
c. where
d. where
e. where
____ 13. Use a computer algebra system and the result “The centroid of the region having area
A bounded by the simple closed path C is ” to find the centroid of
the region bounded by the graphs of and .
a.
b.
932 Chapter 15: Vector Analysis
c.
d.
e.
____ 14. Use a computer algebra system and the result “The area of a plane region bounded by
the simple closed path C given in polar coordinates is ” to find the area of the region
bounded by the graphs of the polar equation .
a.
b.
c.
d.
e.
___ 15. Use a computer algebra system and the result “The area of a plane region bounded by
the simple closed path C given in polar coordinates is ” to find the area of the region
bounded by the graphs of the polar equation . Round your answer to two decimal places.
a.
b.
c.
d.
e.
15.4 Green’s Theorem 933
____ 16. Evaluate , where is the unit circle given by
.
a.
b.
c.
d.
e.
____ 17. Find the maximum value of where C is any closed curve
in the xy-plane, oriented counterclockwise.
a.
b.
c.
d.
e.
934 Chapter 15: Vector Analysis
15.4 Green’s Theorem
Answer Section
MULTIPLE CHOICE