Find an arc length parametrization of r(t) = (e' sin t, e' cos t, 10e*) r:(s) = (| %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Find an arc length parametrization of r(t) = (e' sin t, e' cos t, 10e')
COS
r:(s) = (|
Transcribed Image Text:Find an arc length parametrization of r(t) = (e' sin t, e' cos t, 10e') COS r:(s) = (|
Expert Solution
Step 1

Given the parametrization rt=etsint,etcost,10et.

 

First, let us find the arc length function. It is given by st=0tr'tdt.

rt=etsint,etcost,10etDifferentiating, we getr't=etsint+cost,etcost-sint,10et

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