Can you help me with problems 12, 21 from the last photo. Thanks so much!

. AT&T S 10:17 PM 01 12% SECTION 11.2 Arc Length and Speed 631 11.2 Arc Length and Speed We now derive a formula for the arc length s of a curve in parametric form. Recall that in Section 8.2, are length of a curve C was defined as the limit of the lengths of polygonal approximations of C (Figure 1). at 1 Polygonal approximations to a ant C for N = 5 and N = 10. N -5 N = 10 To compute the length of C via a parametrization, we need to assume that the parametriza tion directly traverses C, that is, the path traces C from one end to the other without changing direction along the way. Thus, assume that c() = (x(1), y()) is a parametriza tion that directly traverses C for a $ 1 s b. We construct a polygonal approximation L consisting of the / segments obtained by joining points Po = c(to), P1 = c(1), .... PN = C(IN) corresponding to a choice of values fo = a + x(> di i=l THEOREM 1 Arc Length Let c(1) = (x(1), y(r)) be a parametrization that directly case of the square root, the are length traverses C for a s t b and set * = / 1 - 1 Use a parametric representation to show that the ellipse ()+ () = . has length L = 4aG(.k). where G(8 . k) = [ VI - k2 sin? i di FIGURE 8 is the elliptic integral of the second kind. 5 /5