In this problem we justify the formula for the length of acurve given on page 932
Chapter 17, Problem 53(choose chapter or problem)
In this problem we justify the formula for the length of acurve given on page 932. Suppose the curve C is givenby smooth parametric equations x = x(t), y = y(t),z = z(t) for a t b. By dividing the parameter intervala t b at points t1,...,tn1 into small segmentsof length t = ti+1 ti, we get a corresponding divisionof the curve C into small pieces. See Figure 17.17,where the points Pi = (x(ti), y(ti), z(ti)) on the curveC correspond to parameter values t = ti. Let Ci be theportion of the curve C between Pi and Pi+1.(a) Use local linearity to show thatLength of Ci x(ti)2 + y(ti)2 + z(ti)2 t.(b) Use part (a) and a Riemann sum to explain whyLength of C =, bax(t)2 + y(t)2 + z(t)2 dt.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer