Math 2414 DHW 7
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School
University of Texas, Dallas *
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Course
2413
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
4
Uploaded by DoctorLightning3936
Ashwin Indurti
Math2414SP24
Assignment DHW
7
–
8.1
8.2
9.3
–
S24 due 03/04/2024 at 11:59pm CST
Problem 1.
(1 point)
Consider the curve defined by the equation
y
=
5
x
4
+
17
x
.
Set
up an integral that represents the length of curve from the point
(
-
3
,
354
)
to the point
(
3
,
456
)
.
Z
dx
Answer(s) submitted:
•
3
•
-3
•
sqrt(1+(20xˆ3+17)ˆ2)
(correct)
Correct Answers:
•
3
•
-3
•
sqrt(1+(20*xˆ3+17)ˆ2)
Problem 2.
(1 point)
Use the arc length formula to find the length of the curve
y
=
5
-
3
x
,
-
3
≤
x
≤
2.
You can check your answer by noting the shape of the curve.
Arc length =
Answer(s) submitted:
•
5sqrt10
(correct)
Correct Answers:
•
5*sqrt(10)
Problem 3.
(1 point)
Use the arc length formula to find the length of the curve
y
=
√
4
-
x
2
, 0
≤
x
≤
2
.
You can check your answer by noting the
shape of the curve.
Arc length =
Answer(s) submitted:
•
pi
(correct)
Correct Answers:
•
2*pi/2
Problem 4.
(1 point)
Find the exact length of the curve
x
=
2
3
(
y
2
-
1
)
3
/
2
, 1
≤
y
≤
4
.
Arc length =
Answer(s) submitted:
•
39
(correct)
Correct Answers:
•
1/3*(1-3*4+2*4ˆ3)
Problem 5.
(1 point)
Find the exact length of the curve
y
=
ln
(
cos
x
)
from
x
=
0 to
x
=
π
/
6
.
Length:
Answer(s) submitted:
•
1/2ln3
(correct)
Correct Answers:
•
ln(sec(pi/6)+tan(pi/6))
Problem 6.
(1 point)
Find the exact length of the curve
x
2
=
11
y
3
between the points
(
0
,
0
)
and
(
121
,
11
)
.
Length:
Answer(s) submitted:
•
(incorrect)
Correct Answers:
•
8/(27*11)*[(9/4*11ˆ2+1)ˆ(3/2)-1]
Problem 7.
(1 point)
Find the exact length of
y
=
1
4
x
2
-
1
2
ln
x
over the interval
[
1
,
8
e
]
.
Length:
Answer(s) submitted:
•
1/4(64eˆ2+2ln(8e)-1)
(correct)
Correct Answers:
•
(8ˆ2*eˆ2+1)/4+[ln(8)]/2
Problem 8.
(1 point)
Find the exact length of the curve
y
=
x
3
6
+
1
2
x
,
1
2
≤
x
≤
1.
Arc length =
Answer(s) submitted:
•
31/48
(correct)
Correct Answers:
•
31/48
1
Problem 9.
(1 point)
Find the arc length of the curve
y
=
1
2
(
e
x
+
e
-
x
)
from
x
=
0 to
x
=
3
.
Length:
Answer(s) submitted:
•
(eˆ6-1)/(2eˆ3)
(correct)
Correct Answers:
•
1/2*[eˆ3-eˆ(-3)]
Problem 10.
(1 point)
Which of the following integrals represents the area of the surface
obtained by rotating the curve
y
=
e
x
,
1
≤
y
≤
2
,
about the
y
-axis?
•
A. 2
π
Z
2
1
y
q
1
+(
1
/
y
)
2
dy
•
B. 2
π
Z
2
1
e
y
q
1
+(
1
/
y
)
2
dy
•
C. 2
π
Z
2
1
ln
(
y
)
p
1
+(
1
/
y
)
dy
•
D. 2
π
Z
2
1
e
y
p
1
+(
1
/
y
)
dy
•
E. 2
π
Z
2
1
ln
(
y
)
q
1
+(
1
/
y
)
2
dy
•
F. 2
π
Z
2
1
y
p
1
+(
1
/
y
)
dy
Answer(s) submitted:
•
B
(incorrect)
Correct Answers:
•
E
Problem 11.
(1 point)
Which of the following integrals represents the area of the surface
obtained by rotating the curve
y
=
ln
(
x
)
,
1
≤
x
≤
3
,
about the
x
-axis?
•
A. 2
π
Z
3
1
x
q
1
+(
1
/
x
)
2
dx
•
B. 2
π
Z
3
1
ln
(
x
)
p
1
+(
1
/
x
)
dx
•
C. 2
π
Z
3
1
ln
(
x
)
q
1
-
(
1
/
x
)
2
dx
•
D. 2
π
Z
3
1
ln
(
x
)
q
1
+(
1
/
x
)
2
dx
•
E. 2
π
Z
3
1
x
q
1
+(
1
/
x
)
2
dx
•
F. 2
π
Z
3
1
x
q
1
+(
1
/
x
)
2
dx
Answer(s) submitted:
•
D
(correct)
Correct Answers:
•
D
Problem 12.
(1 point)
Find the area of the surface generated by rotating
y
=
4
x
+
3,
2
≤
x
≤
4, about the
x
-axis.
S
=
Answer(s) submitted:
•
pi(60sqrt17)
(correct)
Correct Answers:
•
pi*sqrt(17)*60
Problem 13.
(1 point)
Find the area of the surface generated by rotating the curve
x
=
4
+
4
y
2
,
, 0
≤
y
≤
1 about the
x
-axis.
S
=
Answer(s) submitted:
•
-pi/96+(65sqrt(65)pi)/96
(correct)
Correct Answers:
•
2*pi/(3*64)*[65ˆ(3/2)-1]
2
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