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Name: ____________________________ PID: ________________
TA: ______________________ Sec. No: _____ Sec. Time: ______
Math 10B.
Midterm Exam 1
January 29, 2007
Turn off and put away your cell phone
.
Read each question carefully
,
and answer each question completely
.
Show all of your work
.
No credit will be given for unsupported answers
.
Write your solutions clearly and legibly
.
No credit will be given for illegible solutions
.
1.
Find the general antiderivative of each of the following functions.
(a)
(2 points)
f
(
x
) =
x
5
– 2
x
2
+ 3.
()
52
6
3
12
23
3
63
x
xd
x
xx
x
−+
=
−
+
+
∫
C
.
(b)
(2 points)
f
(
x
) = (2
x
+ 1)
2
.
2
2
4
21
4
41
2
3
x
dx
x
x
dx
x
x
x
C
+=
+
+
=
+
+
+
∫∫
.
(c)
(2 points)
5
() 2
fx
x
x
=−
.
( )
1/2
3/2
55
22
4
5ln
3
x
dx
x
dx
x
xC
−=
−
=−+
#
Points
Score
16
24
34
46
20
Σ
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(4 points) The following table gives the velocity of an airplane as it took off from
a runway. If the airplane lifted off the runway after 5 seconds, what are the
minimum and maximum distances the airplane could have covered on the
runway?
Time (sec)
0
1
2
3
4
5
Velocity (feet/sec)
0
10
30
50
70
90
Notice that the velocity is increasing (and this makes sense, seeing that the
airplane is accelerating to take off.) Recall, that distance is the antiderivative of
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