Integration By U-Substitution And Pattern Recognition Worksheet - Ws 4.4, Calculus Maximus
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7Calculus Maximus
WS 4.4: u-sub & pattern recog
Name_________________________________________ Date________________________ Period______
Worksheet 4.4—Integration by u-Substitution and Pattern Recognition
No calculator unless otherwise stated.
Show all work.
Multiple Choice:
1. Find the most general function f such that
f
x
9cos3
x
2
2
(A)
f x
3sin
x Cx
D
(B)
f x
cos3
x Cx D
(C)
f x
3cos3
x Cx
D
(D)
f x
sin
x Cx D
(E)
f x
3sin 3
x Cx D
1
2
x
2. Evaluate the definite integral:
1
e
dx
.
0
3
1
7
2
1
3
1
3
1
2
2
2
(A)
2
e
e
(B)
(C)
2
e
e
(D)
2
e
e
2
2
2
2
e
2
2
2
2
2
e
7
2
1
(E)
2
2
e
2
e
2
f
.
2
x
3. Find the value of
1
when
f x
6
xe
,
f
0
1
5
3
3
3
5
3
5
3
2
2
2
2
2
(A)
e
(B)
e
(C)
e
(D)
e
(E)
e
2
2
2
2
2
2
2
2
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