Stewart_Calc_7ET ch16sec02
MULTIPLE CHOICE
1. Evaluate the line integral
where and C is the arc of the circle traversed
counterclockwise from ( , 0) to (0, ). Round your answer to two decimal places.
a.
b.
c.
d.
e.
2. Find the exact mass of a thin wire in the shape of the helix
if the density is 5.
a.
b.
c.
d.
e.
3. Find the work done by the force field on a particle that moves along the
parabola
a.
b.
c.
d.
e.
4. Evaluate the line integral over the given curve C.
; ,
a.
b.
c.
d.
5. Evaluate the line integral over the given curve C.
; ,
a.
b.
3
c.
1
d.
6. Find the work done by the force field F on a particle that moves along the curve C.
; ,
a.
−138
21
237
−3
−1
7
28
3
b.
c.
d.
7. Evaluate the line integral over the given curve C.
; ,
a.
b.
c.
d.
8. Find the work done by the force field F on a particle that moves along the curve C.
; ,
a.
b.
c.
d.
9. Evaluate , where C is given by Round
your answer to two decimal place.
107
6
52
3
26
3
27
513
4
36
72
17
19
34
71
2
a.
b.
c.
d.
e.
10. Evaluate where C is the right half of the circle
a.
b.
c.
d.
e.
11. A thin wire is bent into the shape of a semicircle If the linear density is ,
find the exact mass of the wire.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find the work done by the force field in moving an object along
an arch of the cycloid
2. Calculate the work done by the force field
when a particle moves under its
influence around the edge of the part of the sphere that lies in the first
octant, in a counterclockwise direction as viewed from above.
3. Find the exact value of where C is the line segment from (0, 0, 0) to (1, , ).
4. Find the exact value of where and C is given by
SHORT ANSWER
1. Evaluate the line integral over the given curve C.
, where C is the line segment joining (–4, –5) to (5, 4)
2. The plot of a vector field is shown below. A particle is moved .
By inspection, determine whether the work done by F on the particle is positive, negative, or
zero.
3. Evaluate the line integral over the given curve C.
, where C is the line segment joining (–2, –1) to (4, 5)
4. A thin wire in the shape of a quarter-circle , , has a linear mass
density . Find the mass and the location of the center of mass of the wire.
5. The plot of a vector field is shown below. A particle is moved .
By inspection, determine whether the work done by F on the particle is positive, negative, or
zero.
