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

emancipezN

Answered question

2021-01-08

Investigation Consider the helix represented by the vector-valued functionr(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 integrals= 0t [x(u)]2 + [y(u)]2 + [z(u)]2 du

Answer & Explanation

crocolylec

crocolylec

Skilled2021-01-09Added 100 answers

To calculate: The length of the arc s on the helix as a function of tThe length of the curve is s= 5t.Used formula: s= 0t [x(t)]2 + [y(t)]2 + [z(t)]2 dtCalculation:The helix path is,r(t)= < 2 cos t, 2 sin t, t >On differentiating this vector value function,r(t)= < 2 sin t, 2 cos t, 1 >Calculate the length of the line segment for the given interval ass= 0t [x(t)]2 + [y(t)]2 + [z(t)]2 dt
= 0t (2 sin t)2 + (2 cos t)2 + (1)2 dt
= 0t 5dt
=5tThus, the arc length is s=5t.

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