Ma 113 Functions And Inverse Functions, The Exponential Function And The Logarithm Worksheet Page 35
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41Worksheet # 27: Substitution and Further Transcendental Functions
1. Evaluate the following indefinite integrals, and indicate any substitutions that you use:
4
3
(a)
dx
(d)
sec
(x) tan(x) dx
3
(1 + 2x)
2
(e)
e sin (e ) dx
3
(b)
x
x
+ 1 dx
2x + 3
4
(c)
cos
(θ) sin(θ) dθ
(f)
dx
2
x
+ 3x
2. Evaluate the following definite integrals, and indicate any substitutions that you use:
7
4
dx
(a)
4 + 3x dx
(d)
x ln x
0
2
1
2
e
(b)
cos(x) cos (sin(x)) dx
(e)
dx
2
x
0
1
4
x
(c)
dx
2
1 + 2x
0
3. Assume f is a continuous function.
9
3
2
(a) If
f (x) dx = 4, find
x f (x
) dx.
0
0
2
2
(b) If
f (x) dx = 1 + e
for all real numbers u, find
f (2x) dx.
0
0
4. Evaluate the following indefinite integrals:
dx
dv
(a)
(d)
x
2
v
v
1
dx
(b)
(e)
e dx
2
1
x
dt
2
(c)
(f)
2e
dx
2
1 + t
ln( )
5. Use the equation b = e
to find the indefinite integral
b dx
dx
6. Find b so that
is equal to
x
1
(a) ln(3)
(b) 3
dx
π
7. Find b such that
=
.
2
1 + x
3
0
8. Which integral should be evaluated using substitution? Evaluate both integrals:
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education