An object moves on a trajectory given by r(t) = (30 cos 3t,30 sin 31) for 0sts x. How far does it travel? The object travels units. (Type an exact answer, using x as needed.)Use a calculator to approximate the length of the following curve. Simplify the arc length integral as much as possible before finding an approximation. r(t) = (5 cost, 20 sint), for Ost= 2n Write the arc length integral and simplify as much as possible. Choose the correct answer below. 2x O A. L=75 (sint + cost) dt OB. L=75 cost dt 2x C. L=5 71+15 cos 2t dt OD. L= 25 sin 2t+ 400 cos 2t dt The length of the curve is approximately | units. (Round to two decimal places as needed.) Textbook Ask my instructor Clear all Check ansySuppose a curve is described by r(t) = (Ah(t), Bh(t)) , for astsb, where A and B are constants and h has a continuous derivative. Complete parts a. through c. below. -. . b a. Show that the length of the curve is 1AZ + B2| | [hi(t)| dt. Choose the correct answer below. 3 b b a b b a b b OC. L= (APWa] + (BW()? at= VAZ + 62 dt = VA2 +BZ | at a b b b. Use part (a) to find the length of the curve x = 313, y = 713, for Ost=4. L = 487.40 (Type an exact answer, using radicals as needed.)Find the length of the line given by r(t) = (2t,71) for astsb. - - . The length of the line is (Type an expression using a and b as the variables. Type an exact answer, using radicals as needed.)