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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
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

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.
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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