CircusRoof.jpg Consider a circular tent whose roof is made of fabric hanging from the rim of the walls of the tent and supported at a central pole. If you look at the curve that the fabric roof forms along any radial cross-section, you will discover a catenary-that is, a hyperbolic cosine. Modeling the roof as the surface of revolution obtained by revolving the curve y = Rcosh(1 – 7), 0 ≤ x ≤ R around the y-axis, which of the following integrals computes its surface area? 2π 2πR u=0 2π 2πR 1 1 af 2πR² 1 u=0 1 =0 2πR² u cosh(1 – u) du 1 Ľ u cosh(1 - u) du u sinh(1 − u) du Co u sinh(1 − u) du 1 L U= =0 u cosh(1 - u) du u sinh(1 − u) du
CircusRoof.jpg Consider a circular tent whose roof is made of fabric hanging from the rim of the walls of the tent and supported at a central pole. If you look at the curve that the fabric roof forms along any radial cross-section, you will discover a catenary-that is, a hyperbolic cosine. Modeling the roof as the surface of revolution obtained by revolving the curve y = Rcosh(1 – 7), 0 ≤ x ≤ R around the y-axis, which of the following integrals computes its surface area? 2π 2πR u=0 2π 2πR 1 1 af 2πR² 1 u=0 1 =0 2πR² u cosh(1 – u) du 1 Ľ u cosh(1 - u) du u sinh(1 − u) du Co u sinh(1 − u) du 1 L U= =0 u cosh(1 - u) du u sinh(1 − u) du
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:CircusRoof.jpg Consider a circular tent whose roof is made of
fabric hanging from the rim of the walls of the tent and supported at a
central pole. If you look at the curve that the fabric roof forms along any
radial cross-section, you will discover a catenary-that is, a hyperbolic
cosine. Modeling the roof as the surface of revolution obtained by
revolving the curve
y = Rcosh(1 – 7), 0 ≤ x ≤ R
around the y-axis, which of the following integrals computes its surface
area?
2π
2πR
u=0
2π
2πR
1
1
af
2πR²
1
u=0
1
=0
2πR²
u cosh(1 – u) du
1
Ľ
u cosh(1 - u) du
u sinh(1 − u) du
Co
u sinh(1 − u) du
1
L
U= =0
u cosh(1 - u) du
u sinh(1 − u) du
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