Integration By U-Substitution And Pattern Recognition Worksheet - Ws 4.4, Calculus Maximus Page 6
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7Calculus Maximus
WS 4.4: u-sub & pattern recog
13. Evaluate the following definite integrals without a calculator.
1
2 / 3
3
3
5
3
4
2
(a)
(b)
x
sin
x
dx
(c)
(d)
x
1
x
dx
7 3xdx
x
1
xdx
0
1
0
/ 4
1
1
3
x
1
e
1
2
(e)
cos
sin
d
(f)
dx
(g)
dx
3
x
2
5
5
e
3
x
1 9
x
0
0
0
14. Use u-substitution to answer the following:
1
dx
x
(a) If
tan
C
,
find
dx
exactly where C is a constant.
x
1 cos
x
2
3 3cos
4
2
x
x
(b) If
dx
, find
dx
exactly.
x
5
x
12
e
1
e
1
0
0
Page 6 of 7
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