Name: __________________
Class:
1 A particle is moved along the x axis by a force that measures
4
(1 + x)
pounds at a point x feet from the origin. Find the
2
work done in moving the particle from the origin to a distance of
3 ft.
________ J
2 Find the work done in pushing a car a distance of 7 m while
exerting a constant force of 900 N.
________ J
3 A spring has a natural length of 40 cm. If a 11 N force is
required to keep it stretched to a length of 50 cm, how much work
is required to stretch it from 40 cm to 45 cm?
Please give the answer to two decimal places.
________ J
4 A heavy rope, 40 ft long, weighs 0.5 lb/ft and hangs over the edge
of a building 120 ft high.
Please round your answers to two decimal places.
(a) How much work is done in pulling the rope to the top of the
building?
________ ft lb
(b) How much work is done in pulling half the rope to the top of
the building?
Date: _____________
6 Newton's Law of Gravitation states that two bodies with masses
m and m attract each other with a force F=G
1
5 A tank is full of water. Find the work required to pump the water
out of the outlet.
1
2
r
where r
Use Newton's Law of Gravitation to compute the work required
to launch a 2000 kg satellite vertically to an orbit 1800 km high.
24
You may assume that Earth's mass is 5.98 10 kg and is
concentrated at its center. Take the radius of Earth to be
6
6.37 10 m and G = 6.67 10
7 Find c such that f
f (x) = ( x ave
11
2
N m /kg
2
= f (c) .
2
3) , [1, 7]
________
8 In a certain city the temperature (in F ) t hours after 8 A.M. was
modeled by the function
T (t) = 46 + 17sin t
12
Find the average temperature (in F ) during the period from 8
A.M. to 8 P.M.
Please round your answer to nearest integer.
F
9 Find the average value of the function on the given interval.
g(x) = 9cos x ,
0, 2
Enter the answer as an expression using the symbol decimal rounded to two places.
PAGE 1
2
2
is the distance between the bodies and G is the gravitational
constant.
________
________ ft lb
m m
, or as a
Name: __________________
Class:
Date: _____________
10 Evaluate the integral.
sin
1
13 Use the method of cylindrical shells to find the volume
generated by rotating the region bounded by the given curves
about the specified axis.
(10x)dx
x
y = e , y = e
xsin
a.
b.
xsin
2
1
1
(10x) + 1
10
(10x) 1
1 x sin
d.
1 x 2 sin 10
e.
1 xsin 10
1
1
2
1 100x
(10x) 1 1 1 +C
100x
1
10
(10x) + 1
10
2
2
+ C
100x
100x
2
, x = 8 ; about the y axis
2
6
cos 3
d
0
15 Evaluate the integral.
4 + C
+ C
4sin x dx
cos x
16 Evaluate the integral.
3
11 Evaluate the integral.
x
14 Evaluate the integral.
+ C
3
(10x) + 1
10
c.
100x
5
tan (9x) sec (9x) dx
2
p ln pdp
1 p3 + C
3
a.
1 sec 7 (9x) + 1 sec 5 (9x) + C
63
45
b.
1 csc 7 (9x) 63
1 csc 5 (9x) + C
45
a.
1 p 3 ln p 3
b.
1 p 3 ln p + 1 p 3 + C
2
2
c.
1 sec 7 (9x) 63
1 sec 5 (9x) + C
45
c.
1 p 3 ln p 3
d.
1 sec 7 (9x) 63
1 csc 5 (9x) + C
45
d.
1 p 3 ln p + 1 p 2 + C
3
4
e.
1 csc 7 (9x) + 1 csc 5 (9x) + C
63
45
e.
1 p 3 ln p 2
1 p3 + C
9
1 p3 + C
4
17 Find the area of the region bounded by the given curves.
3
y = sin 3x, y = sin 3x, x = 0, x = 12 First make a substitution and then use integration by parts to
evaluate the integral.
81
e
x
18 Evaluate the integral.
dx
49
9
7
d.
21e
9
7
e.
20e + 12e
a.
17e + 12e
b.
17e + 13e
c.
16e
PAGE 2
9
12e
7
9
9
13e
7
7
xe
8x
dx
6
Name: __________________
Class:
Date: _____________
19 Evaluate the integral.
e
22 Evaluate the integral.
a.
11 e 122
b.
11 e 122
c.
11 e 122
d.
11 e 122
e.
1 e
122
1 e
121
sin 11
sin 11
1 e
122
11 e 122
sin 11
sin 11
+
1 e
121
sin 11
+
1 e
122
sin c x dx
cos 11
+ C
a.
1 cos 3 cx 3c
cos 11
+ C
b.
1 sin 4 cx + C
4c
cos 11
+ C
c.
1 cos cx + C
c
1 cos 4 cx + C
4c
cos 11
+ C
d.
1 sin 3 cx 3c
1 sin cx + C
c
cos 11
+ C
e.
1 sin 3 cx 3c
1 cos cx + C
c
20 Suppose that f (5) = 3 , f (9) = 7 , f' (5) = 8 ,
f' (9) = 5 , and f' ' is continuous. Find the value of
3
cos 11 d
23 Evaluate the integral.
9
1 xf' ' (x) dx .
5
________
2
tan 8x dx
2
sec 8x
24 Evaluate the integral.
21 Evaluate the integral.
5
dx
cos 9x 4
cos 9x sin 9x dx
1
25 Evaluate the indefinite integral.
a.
1 sin 5 9x 45
2 sin 7 9x + 1 sin 9 9x + C
63
81
b.
1 cos 5 9x 45
2 cos 7 9x + 1 cos 9 9x + C
63
81
5
c.
1 cos 9x 45
5
d.
1 sin 9x 45
5
e.
1 sin 9x 45
7
9
7
9
7
9
1 cos 9x + 1 cos 9x + C
63
81
1 cos 9x + 1 sin 9x + C
63
81
1 sin 9x + 1 sin 9x + C
63
81
4
sec x dx
5
a.
5 tan 3 x + 5tan x + C
3
5
5
b.
3
5tan x + 5tan x + C
5
5
c.
5 tan 3 x + 5 tan x + C
3
5
3
5
d.
5 tan 3 x 3
5
e.
PAGE 3
5tan x 5
5tan x + C
5
5 tan 3 x + C
3
5
Name: __________________
Class:
26 Evaluate the integral.
2
tan 4x sec 4x dx
a.
1 ( sec 4x tan 4x 8
b.
1 ( ln sec 4x tan 4x
8
c.
1 ( sec 4x + tan 4x 8
d.
1 ( sec 4x tan 4x + ln sec 4x + tan 4x ) + C
8
e.
1 ( sec 4x 8
PAGE 4
ln sec 4x + tan 4x ) + C
ln sec 4x + tan 4x ) + C
ln sec 4x + tan 4x ) + C
tan 4x + ln sec 4x tan 4x ) + C
Date: _____________