# Investigation Consider the helix represented by the vector-valued function r(t)= < 2 cos t, 2 sin t, t > (a) Write the length of the arc son the helix as a function of t by evaluating the integral s= int_{0}^{t} sqrt{[x'(u)]^{2} + [y'(u)]^{2} + [z'(u)]^{2} du}

emancipezN 2021-01-08 Answered
Investigation Consider the helix represented by the vector-valued function(a) Write the length of the arc son the helix as a function of t by evaluating the integral
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## Expert Answer

crocolylec
Answered 2021-01-09 Author has 100 answers
To calculate: The length of the arc s on the helix as a function of tThe length of the curve is Used formula: Calculation:The helix path is,On differentiating this vector value function,Calculate the length of the line segment for the given interval as

$=\sqrt{5t}$Thus, the arc length is $s=\sqrt{5t}.$
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