Larson_Calculus_10e ch15sec04
MULTIPLE CHOICE
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.
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.
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.
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.
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.
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.
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.