Consider the path r(t) = ( 1, 1, 14) with 1 [0, 2]. (a) Show...

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Consider the path r(t) = ( 1², 1³, 14) with 1 € [0, 2]. (a) Show that for this path, the infinitesimal element of (arc)length ds is given by ds = (t +21³) dt. (b) Calculate the length of this path for t = [0, 2]. Hints: (i) The simple expression for ds in Part (a) involves recasting a quadratic expression of t as a square and simplifying; (ii) The result stated in Part (a) may be used to complete Part (b). Consider the path r(t) = ( 1², 1³, 14) with 1 € [0, 2]. (a) Show that for this path, the infinitesimal element of (arc)length ds is given by ds = (t +21³) dt. (b) Calculate the length of this path for t = [0, 2]. Hints: (i) The simple expression for ds in Part (a) involves recasting a quadratic expression of t as a square and simplifying; (ii) The result stated in Part (a) may be used to complete Part (b).

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a The infinitesimal element of arclength ds is ... View the full answer