University of Ottawa -
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School
University of Ottawa *
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Course
1330A
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
6
Uploaded by HighnessRoseGuineaPig14
2023-11-30, 11
:
54 PM
University of Ottawa -
Page 1 of 6
file:///Users/bharat/Desktop/University%20of%20Ottawa%20-%20inegral%20practice.html
Online Homework System
Assignment Worksheet
11/30/23 - 6:52:24 PM EST
Name:
____________________________
Class:
MAT1330A : Calculus for the Life
Sciences I, Fall 2023
Class #:
____________________________
Section #:
____________________________
Instructor:
Monica Nevins
Assignment:
Homework 9 Fall 2023
Question 1: (1 point)
Using the method of substitution, determine which of the following represents .
(a)
(b)
(c)
(d)
Question 2: (1 point)
Setting , which of the following is equivalent to ?
(a)
(b)
(c)
(d)
∫
dx
2
x
1 +
x
4
+
C
x
2
x
+
1
5
x
5
arctan(
) +
C
x
2
+
C
x
2
1 +
x
4
ln(1 +
) +
C
x
2
x
4
u
=
x
2
∫
ln(
)
dx
x
3
x
4
∫
ln(
)
du
1
2
u
u
2
∫
ln(
)
du
1
3
u
u
3
∫
ln(
)
du
1
2
u
2
u
2
∫
ln(
)
du
1
3
u
2
u
2
1
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54 PM
University of Ottawa -
Page 2 of 6
file:///Users/bharat/Desktop/University%20of%20Ottawa%20-%20inegral%20practice.html
(e)
(f)
Question 3: (1 point)
Setting , which of the following is equivalent to ?
(a)
(b)
(c)
(d)
(e)
(f)
Question 4: (1 point)
With the substitution , we get
where the resulting integrand is __________ .
FORMATTING: We write trigonometric powers in long form in Mobius. For example is written .
∫
ln(
)
du
1
2
u
u
3
∫
ln(
)
du
1
3
u
u
2
u
=
x
2
∫
dx
tan(
)
x
8
x
3
∫
du
1
3
tan(
)
u
4
u
2
∫
du
1
2
tan(
)
u
5
u
2
∫
du
1
2
tan(
)
u
4
u
∫
du
1
3
tan(
)
u
4
u
∫
du
1
3
tan(
)
u
5
u
2
∫
du
1
2
tan(
)
u
4
u
2
u
= sin(5
x
)
∫
d
x
=
∫
f
(
u
)d
u
cos(5
x
)
(5
x
)
sin
3
f
(
u
) =
(
x
)
cos
2
(cos(
x
))
2
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:
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University of Ottawa -
Page 3 of 6
file:///Users/bharat/Desktop/University%20of%20Ottawa%20-%20inegral%20practice.html
Question 5: (1 point)
Compute the indefinite integral
__________ where is the constant of integration. Do not include the constant of integration in your answer as we have already done so.
Question 6: (1 point)
Compute the indefinite integral
__________ where is the constant of integration. Do not include the constant of integration in your answer as we have already done so.
Question 7: (1 point)
Compute the indefinite integral
__________ where is the constant of integration. Do not include the constant of integration in your answer as we have already done so.
∫
dx
=
(3
x
+ 3)
3
+
C
C
∫
dx
=
e
x
+ 1
e
x
+
C
C
∫
dx
=
e
x
(2 + 4
)
e
x
2
+
C
C
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