To illustrate that the length of a smooth space curve does not depend on the parametrization you
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To illustrate that the length of a smooth space curve does not depend on the parametrization you use to compute it, calculate the length of one turn of the helix in Example 1 with the following parametrizations.
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a. r(t) = (cos 4t)i + (sin 4t)j + 4tk, 0≤t≤ π/2 b. r(t) = [cos (t/2)] + [sin (t/2)]j + (t/2)k, 0≤ t ≤ 4π c. r(t) = (cos t)i - (sin t)j - tk, -2π ≤ t ≤0
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To calculate the length of a smooth space curve we can use the arc length formula L dxdt dydt dzdt d...View the full answer
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Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
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