Find the distance travel 33. Find the area bounded by the curve x = cost, y = e', (x, y) as i varies in the given tim 0 1 7/2, and the lines y = 1 and x = 0. length of the curve. 51. x = sin't, y = cost, 34. Find the area of the region enclosed by the astroid x = a cos 0, 0 y = a sin'0. (Astroids are explored in the Laboratory Project 52. x = cos't, y = cost, 0 on page 695.) 35. Find the area under one arch of the trochoid of Exercise 38 in 53. Show that the total length Section 1 1.1 for the case d b > 0, is 36. Let OR be the region enclosed by the loop of the curve in Example 1. L = 4a (a) Find the area of R. (b) If R is rotated about the x-axis, find the volume of the where e is the eccentricity resulting solid. c = Vaz - b2). (c) Find the centroid of R. 54. Find the total length of th where a > 0. 37-40 Ill Set up, but do not evaluate, an integral that represents the length of the curve. CAS 55. (a) Graph the epitrochoi 37. x = 1 - 12, y = 313/2, 1six2 x = 11 c 38. x = 1 + e', y=12, - 351=3 y = 1l s 39. x = 1+ cost, y = t - sint, Ost= 21 What parameter inte 40. x = Int, y = Vt+1, Ists5 (b) Use your CAS to fin D CAS 56. A curve called Cornu's equations 41-44 Ill Find the length of the curve. x = CC 41. * = 1+ 312, y = 4+2+3, Ost= 1 42. x = a(cos 0 + 0 sin 0), y = a(sin @ - 0 cos 0), y = S(t where C and S are the 43. x = y = In(1 + t), Ost=2 Chapter 5. 1 + t' (a) Graph this curve. (b) Find the length of 44. x = e'+ e, y = 5 - 21, Ost b > 0, is L = 4a - V1 -e2 sin20 do where e is the eccentricity of the ellipse (e = c/a, where he c = Vaz - b2). 54. Find the total length of the astroid x = a cos'0, y = a sin'0, where a > 0. ents the CAS 55. (a) Graph the epitrochoid with equations x = 1 1 cost - 4 cos(1 1t/2) y = 11 sin t - 4 sin(1 1/2) What parameter interval gives the complete curve? (b) Use your CAS to find the approximate length of this curve. CAS 56. A curve called Cornu's spiral is defined by the parametric