12) Using the parametric arc length formula, find the arc length for the following parametric equation...
2. (10 points) Find the arc length of the following paths. (The length of the path e(t) for to st<t is L = S ||'(t)||dt) (a) (5 points) c(t) = (t +1, 24243/2, {{2) for 1sts2
Find the parametric equation of a circle of radius R, centered at (x = a; y = b), using the arc length as a parameter.
number 9
9) Let C be the arc of the circle: x +y-9 from (3.0) to a) Find a parametric equation of a circle of radius r 3 that starts at (3,0) and has a counterclockwise orientation b) Find the interval fort that sketches the arc from (3,0) to G. c) Use your limits from part(b) to calculate the area of the surface of revolution by revolving the curve C about the x-axis.
9) Let C be the arc of...
(a) Use a graphing utility to graph the curve represented by the following parametric 6. x y over the interval -2sts2. (b) Write an integral that represents -3t-1 the arc length of this curve over the interval -2sts2. (Do not attempt to evaluate this integral algebraically.) (c) Use the numerical integration capability of a graphing utility to approximate the value of this integral. Round your result to the nearest tenth. (Be careful with your notation, show orientation arrows on your...
Problem 5. Prove that parametric equations: x a-cosh(s) (a > 0) or back half(a < 0) of hyperboloid of one sheet: Χ t), y b-sinh(s) cos (t) zc-sinh(s) sin( t), (x,y,z) lies on the front half L" a2 b2 c2 Problem 6 What graph of this Compute the arc length : rit)- < sin t, cos t, 2Vt', when 0<t < function: a) Compute the arc length : re)-3cos(9) and 0 < θ < π/2 b) Problem 7. Find parametric...
Find the arc length of the curve y - x over the interval 1,12 (a) 8 points Using the Fundamental Theorem, Part 2 (b) 2 points Use your "DEFINT" program to find M,1, T1 and Sz2 (c) 2 points Using your TI-84's built-in Integral calculator using MATH >>> MATH >>9: fnlnt (d) 2 points In your text book, there are formulas that give the maximum er in approximations given by MN, T, and Sy for the integral A a f(x)...
6. (a) Use a graphing utility to graph the curve represented by the following parametric x=езі, over the interval-2sts2.(b) Write an integral that represents tions: the arc length of this curve over the interval -2sts2. (Do not attempt to evaluate this integral algebraically) (e) Use the numerical integration capability of a the value of this integral. Round your result to the nearest tenth (Be careful with your notation, show orientation arrous on your curve, and show your steps clearly.) utility...
Find the arc length of the curve below on the given interval. X 1 y= on (1,3] 4 2 8x The length of the curve is (Type an exact answer, using radicals as needed.)
Use the Arc Length formula to find the exact length of the curve and leave the answer in fraction:- y(x2 - 438/2, 25x54
Use the arc length formula to find the length of the curve y = 4x - 5, -1 sxs 2. Check your answer