32. Find an arc length parametrization of the curve parametrized by %3D r(1) = (1,/2, 32), with the parameter s measuring from (0, 0,0).
32. Find an arc length parametrization of the curve parametrized by %3D r(1) = (1,/2, 32), with the parameter s measuring from (0, 0,0).
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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Question
Number 32

Transcribed Image Text:32. Find an arc length parametrization of the curve parametrized by
with the parameter s measuring from (0, 0, 0).
33. Find an arc length parametrization of the curve parametrized by
6.
r(t) = (cos t, sin t, t/2), with the parameter s measuring from (1,0, 0).
r(t) = (e' sin t, e' cos t, e').
34. Find an arc length parametrization of the curve parametrized by
%3D
35. Find an arc length parametrization of the curve parametrized by
%3D
36. Find an arc length parametrization of the cycloid with parametrization
r(t) = (t- sin t, 1- cos t).
%3D
37. Find an arc length parametrization of the line y = mx for an arbitrary
38. Express the arc length L of y = x' for 0 < x < 8 as an integral in two
ways, using the parametrizations rị(t) = (1,1°) and r2(t) = (t³,1°). Do not
evaluate the integrals, but use substitution to show that they yield the same
%3D
%3D
result.
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