The roof of a silo is made by revolving the following curve from x=0 to x=5 about the y-axis: y = f(x) = 10 cos 10 cos (*) The surface area S, that is obtained by revolving a curve y=f(x) in the domain from a to b Around the y-axis, can be calculated by Pappus theorem: S = 2T ET S IV √1+[f'(x)]²dx. Calculate the surface area using the following methods with 9 subintervals each: a. Rectangular method b. Trapezoidal method. c. Simpson's 1/3 Rule d. Simpson's 3/8 Rule Compare the results with the exact analytical integral.
The roof of a silo is made by revolving the following curve from x=0 to x=5 about the y-axis: y = f(x) = 10 cos 10 cos (*) The surface area S, that is obtained by revolving a curve y=f(x) in the domain from a to b Around the y-axis, can be calculated by Pappus theorem: S = 2T ET S IV √1+[f'(x)]²dx. Calculate the surface area using the following methods with 9 subintervals each: a. Rectangular method b. Trapezoidal method. c. Simpson's 1/3 Rule d. Simpson's 3/8 Rule Compare the results with the exact analytical integral.
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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![The roof of a silo is made by revolving the following curve from x=0 to
x=5 about the y-axis:
y = f(x) = 10 cos(x)
The surface area S, that is obtained by revolving a curve y=f(x) in the
domain from a to b Around the y-axis, can be calculated by Pappus
theorem:
STV
I√1+f'(x)]²dr.
S = 2π
Calculate the surface area using the following methods with 9
subintervals each:
a. Rectangular method.
b. Trapezoidal method
c. Simpson's 1/3 Rule
d. Simpson's 3/8 Rule
Compare the results with the exact analytical integral.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F623e2369-d075-491b-b7e3-f0a252990dd4%2Fba0e0ed4-0060-4747-a2de-03c4206e175b%2F68ulpef_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The roof of a silo is made by revolving the following curve from x=0 to
x=5 about the y-axis:
y = f(x) = 10 cos(x)
The surface area S, that is obtained by revolving a curve y=f(x) in the
domain from a to b Around the y-axis, can be calculated by Pappus
theorem:
STV
I√1+f'(x)]²dr.
S = 2π
Calculate the surface area using the following methods with 9
subintervals each:
a. Rectangular method.
b. Trapezoidal method
c. Simpson's 1/3 Rule
d. Simpson's 3/8 Rule
Compare the results with the exact analytical integral.
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