Math 2414 DHW 5
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School
University of Texas, Dallas *
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Course
2413
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
3
Uploaded by DoctorLightning3936
Ashwin Indurti
Math2414SP24
Assignment DHW
5
–
7.4
–
S24 due 02/19/2024 at 11:59pm CST
Problem 1.
(1 point)
Evaluate the integral.
Z
-
3
r
2
r
+
4
dr
=
Answer(s) submitted:
•
-3(((r+4)ˆ2)/2-8(r+4)+16ln|r+4|)+c
(correct)
Correct Answers:
•
-1.5*rˆ2--12*r+-48*ln(r+4)+C
Problem 2.
(1 point)
Evaluate the integral.
Z
9
x
4
+
7
x
3
+
13
x
2
+
9
x
+
11
x
2
+
1
dx
=
Answer(s) submitted:
•
3xˆ3+7/2xˆ2+4x+ln|xˆ2+1|+7arctanx+7/2+c
(correct)
Correct Answers:
•
4*x+7*xˆ2/2+9*xˆ3/3+2*ln(xˆ2+1)/2+7*atan(x)+C
Problem 3.
(1 point)
Find the area of the region under the curve
y
=
4
x
+
4
x
-
1
from
x
=
2
to
x
=
3
.
Area =
Answer(s) submitted:
•
4[(2+2ln|2|)-(1)]
(correct)
Correct Answers:
•
4*[1+2*ln(2)]
Problem 4.
(1 point)
Which of the following is the correct form of the partial fraction
decomposition of
2
x
(
x
+
3
)(
3
x
+
1
)
?
•
A.
Ax
+
B
x
+
3
+
C
3
x
+
1
•
B.
A
x
+
3
+
Bx
+
C
3
x
+
1
•
C.
A
x
+
3
+
B
3
x
+
1
•
D.
Ax
+
B
x
+
3
+
Cx
+
D
3
x
+
1
Answer(s) submitted:
•
C
(correct)
Correct Answers:
•
C
Problem 5.
(1 point)
Evaluate the indefinite integral.
Z
-
1
x
2
-
10
x
+
25
dx
=
Answer(s) submitted:
•
1/(x-5)+c
(correct)
Correct Answers:
•
1/[x+(-5)]+C
Problem 6.
(1 point)
Evaluate the integral.
Z
6
x
+
8
x
2
+
5
x
-
6
dx
=
Answer(s) submitted:
•
2ln|x-1|+4ln|x+6|+c
(correct)
Correct Answers:
•
ln(|(x-1)ˆ2*(x+6)ˆ4|)+C
1
Problem 7.
(1 point)
Evaluate the integral.
Z
0
-
1
8
x
+
39
x
2
+
11
x
+
24
dx
=
Answer(s) submitted:
•
3ln3+12ln2-5ln7
(correct)
Correct Answers:
•
3*ln(3/2)+5*ln((5+3)/(5+2))
Problem 8.
(1 point)
Evaluate the indefinite integral.
Z
x
3
+
15
x
2
+
4
x
+
3
dx
=
Answer(s) submitted:
•
(incorrect)
Correct Answers:
•
xˆ2/2+(-4)*x+6*ln(|x+3|)+7*ln(|x+1|)+C
Problem 9.
(1 point)
Which of the following is the correct form of the partial fraction
decomposition of
x
-
1
x
3
+
x
2
?
•
A.
Ax
+
B
x
+
Cx
+
D
x
2
+
Ex
+
F
x
+
1
•
B.
A
x
+
B
x
2
+
C
x
+
1
•
C.
Ax
+
B
x
+
Cx
+
D
x
2
+
E
x
+
1
•
D.
Ax
+
B
x
+
Cx
+
D
x
2
+
Ex
+
F
x
+
1
Answer(s) submitted:
•
B
(correct)
Correct Answers:
•
B
Problem 10.
(1 point)
Evaluate the integral.
Z
x
2
(
x
+
7
)
3
dx
=
Answer(s) submitted:
•
(-xˆ2)/(2(x+7)ˆ2)+ln|x+7|+7/(x+7)+c
(correct)
Correct Answers:
•
-49/[2*(x+7)ˆ2]+14/(x+7)+ln(|x+7|)+C
Problem 11.
(1 point)
Evaluate the integral.
Z
-
9
x
4
-
x
2
dx
=
Answer(s) submitted:
•
-9(1/x-0.5ln|x+1|+.5ln|x-1|)+c
(correct)
Correct Answers:
•
-9*[1/x+0.5*ln(|x-1|/|x+1|)]+C
Problem 12.
(1 point)
Which of the following is the correct form of the partial fraction
decomposition of
x
4
x
4
-
1
?
•
A. 1
+
A
x
+
1
+
B
x
-
1
+
C
x
2
+
1
•
B. 1
+
A
x
+
1
+
B
x
-
1
+
Cx
+
D
x
2
+
1
•
C.
-
1
+
A
x
+
1
+
B
x
-
1
+
Cx
+
D
x
2
+
1
•
D.
-
1
+
A
x
+
1
+
B
x
-
1
+
C
x
2
+
1
Answer(s) submitted:
•
B
(correct)
Correct Answers:
•
B
Problem 13.
(1 point)
Which of the following is the correct form of the partial fraction
decomposition of
2
x
+
1
(
x
+
1
)
3
(
x
2
+
4
)
2
?
•
A.
A
x
+
1
+
B
(
x
+
1
)
2
+
Cx
+
D
x
2
+
4
+
Ex
+
F
(
x
2
+
4
)
2
+
Gx
+
H
(
x
2
+
4
)
3
•
B.
A
x
+
1
+
B
(
x
+
1
)
2
+
C
(
x
+
1
)
3
+
Dx
+
E
x
2
+
4
+
Fx
+
G
(
x
2
+
4
)
2
•
C.
Ax
+
B
x
+
1
+
Cx
+
D
(
x
+
1
)
2
+
Ex
+
F
(
x
+
1
)
3
+
Gx
+
H
x
2
+
4
+
Ix
+
J
(
x
2
+
4
)
2
•
D.
A
(
x
+
1
)
3
+
Bx
+
C
(
x
2
+
4
)
2
Answer(s) submitted:
•
B
(correct)
Correct Answers:
•
B
2
Problem 14.
(1 point)
Evaluate the integral.
Z
-
6
(
x
-
2
)(
x
2
+
4
)
dx
=
Answer(s) submitted:
•
-3/2(.5ln|x/2-1|+.5(-.5ln|(xˆ2)/4+1|-arctan(x/2)))+C
(correct)
Correct Answers:
•
-6*[0.125*ln(|x-2|)-0.0625*ln(xˆ2+4)-0.125*atan(x/2)]+C
Problem 15.
(1 point)
Evaluate the integral.
Z
2
x
2
-
4
x
-
2
(
x
-
1
)
2
(
x
2
+
1
)
dx
=
Answer(s) submitted:
•
2ln|x-1|+2/(x-1)-ln|xˆ2+1|+2arctanx+c
(correct)
Correct Answers:
•
2*[ln(|x-1|)+1/(x-1)-0.5*ln(xˆ2+1)+atan(x)]+C
Problem 16.
(1 point)
Evaluate the integral.
Z
-
8
x
4
-
8
x
(
x
2
+
1
)
2
dx
=
Answer(s) submitted:
•
-8/(xˆ2+1)-8lnx+c
(correct)
Correct Answers:
•
-8*[ln(|x|)+1/(xˆ2+1)]+C
Problem 17.
(1 point)
Evaluate the integral.
Z
9
x
3
+
9
x
2
+
18
x
+
9
(
x
2
+
1
)(
x
2
+
2
)
dx
=
Answer(s) submitted:
•
4.5ln|xˆ2+1|+9/sqrt2arctan(x/sqrt2)+c
(correct)
Correct Answers:
•
ln(xˆ2+2)*9-0.5*ln(xˆ2+2)*18+6.36396*atan(0.707107*x)-0.5*
Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America
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