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Find an arc length parametrization of the line y = 4x + 6.

Find an arc length parametrization of the line y = 4x + 6.

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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Find an arc length parametrization of the line y = 4x + 6. Consider the following approach to find the parametrization r(s). Step 1: Let r(t) = (t, 4t + 6) Then, Step 2: r' (t) = (1,4) and ||r' (t)|| = √√/17 Now, Step 3: s(t) = [[ *|\r' = ['|' (u) (u) Finally, du du = [' VTT du = 1 √TI = Step 4: r₁(s) = = (t√/17,4√/17t+6) At which step did an error occur? Explain. Step 3, s(t) is found by integrating the argument r' (u) ||r' (u)|| Step 4, the parametrization is r (g¯¹(s)) where t = g¯¹(s). Step 2, the magnitude of r(t) should be 17. Step 1, the parametrization of the line y = 4x + 6 is wrong.
Transcribed Image Text:Find an arc length parametrization of the line y = 4x + 6. Consider the following approach to find the parametrization r(s). Step 1: Let r(t) = (t, 4t + 6) Then, Step 2: r' (t) = (1,4) and ||r' (t)|| = √√/17 Now, Step 3: s(t) = [[ *|\r' = ['|' (u) (u) Finally, du du = [' VTT du = 1 √TI = Step 4: r₁(s) = = (t√/17,4√/17t+6) At which step did an error occur? Explain. Step 3, s(t) is found by integrating the argument r' (u) ||r' (u)|| Step 4, the parametrization is r (g¯¹(s)) where t = g¯¹(s). Step 2, the magnitude of r(t) should be 17. Step 1, the parametrization of the line y = 4x + 6 is wrong.
Incorrect Compute the actual arc length parametrization of the line. (Enter your answer in the form of a vector (*, *). Enter numbers in exact form. Use symbolic notation and fractions where needed.) r₁(s) = (t,4t+6) Incorrect
Transcribed Image Text:Incorrect Compute the actual arc length parametrization of the line. (Enter your answer in the form of a vector (*, *). Enter numbers in exact form. Use symbolic notation and fractions where needed.) r₁(s) = (t,4t+6) Incorrect
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