An overpass has the form that appears in the following figure: SA A AD 0.75 0st 0.25 O 025 05 0.75 1 125 15 1.75 2 225 2.5 2.75 3 3.25 3.5 -0.25 -05t -0.75t Assuming the hump has the shape of the graph of the function y = y(x) = xe^-x from x = 0 until x = 3 a) Approximately calculate the length of the overpass. b) Obtain a better approximation than that obtained in (a) for the length of the hump by dividing the arc of the graph into four pieces. c) Using the assumption in part (b), obtain a better approximation for the length of the graph, now dividing it into 10 portions. d) With the assumption of part (b), raise the Integral that represents the exact value of the length of that overpass e) Use a technological resource to obtain the exact value
An overpass has the form that appears in the following figure: SA A AD 0.75 0st 0.25 O 025 05 0.75 1 125 15 1.75 2 225 2.5 2.75 3 3.25 3.5 -0.25 -05t -0.75t Assuming the hump has the shape of the graph of the function y = y(x) = xe^-x from x = 0 until x = 3 a) Approximately calculate the length of the overpass. b) Obtain a better approximation than that obtained in (a) for the length of the hump by dividing the arc of the graph into four pieces. c) Using the assumption in part (b), obtain a better approximation for the length of the graph, now dividing it into 10 portions. d) With the assumption of part (b), raise the Integral that represents the exact value of the length of that overpass e) Use a technological resource to obtain the exact value
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:An overpass has the form that appears in the following figure:
y
1T
0.75+
05
0.25
0 025 05 0.75 1
125 15
1.75 2
2.25 2.5 2.75 3
3.25 3.5
-0.25t
-05t
-0.75t
Assuming the hump has the shape of the graph of the function y = y(x) = xe^-x from x = 0
%3D
until x = 3
a) Approximately calculate the length of the overpass.
b) Obtain a better approximation than that obtained in (a) for the length of the hump by
dividing the arc of the graph into four pieces.
c) Using the assumption in part (b), obtain a better approximation for the length of the graph,
now dividing it into 10 portions.
d) With the assumption of part (b), raise the Integral that represents the exact value of the
length of that overpass
e) Use a technological resource to obtain the exact value
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