Integration By U-Substitution And Pattern Recognition Worksheet - Ws 4.4, Calculus Maximus Page 7
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7Calculus Maximus
WS 4.4: u-sub & pattern recog
15. If
ln(
a b
cos( ))
x dx
2 ln(2),
for some positive a and b, find the exact value of
0
5
ln(
a b
cos(5 ))
x dx
.
0
b
16. If
f x dx
( )
K
, evaluate the following integrals in terms of K using your knowledge of
a
transformations.
b
b
5
b
5
x dx
(a)
(b)
(c)
f x
(
5)
dx
[ ( ) 5]
f x
dx
f
(5 )
a
a
5
a
5
6
f z dz
17. If
( )
4
, evaluate the following integrals exactly by using appropriate substitution and limits.
3
2
2
7
(a)
f
(3 )
z dz
(b)
f
(7 2 )
z dz
(c)
( (
f z
1) 5)
dz
1
0.5
4
Page 7 of 7
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