Find the formula for the arc length of the curve x = 2 cost, y = 3 sint, T ≤ t ≤ 3. Then use a ㅠ left Riemann sum with n = 1000 to approximate the arc length. Round your answer to four decimal places.
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- Compute the following problems. Express the answers to 1 decimal place. Use: T=LFN A slot 812.00 millimeters long is cut into a carbon steel baseplate with a feed of0.80 millimeter per revolution. Find the cutting time using a 75-millimeter diameter carbide milling cutter running at 640 r/min.a) Find the arc length of the catenary y = coshx between x = 0 and x = ln4.Use Simpson's Rule with n = 10 to estimate the arc length of the curve. (Round your answer to four decimal places.) y = e−x2, 0 ≤ x ≤ 6
- Find the arc length of the graph of the function y=ln(ex+1ex−1)y=ln(ex+1ex−1) over the interval [[ ln(2),ln(3)ln(2),ln(3) ]]Set up the definite integrals to compute the arc length and the surface area formed by rotating the function about the given line on the interval. y=x^2 on [0,2] rotated about the y-axisThe length of the arc of y = ln cos x from x = π/4 to x = π/3 equals______.
- Find the arc length of the portion of the graph of y=x2+x , where −1≤x≤1 You may numerically approximate the arc length after setting the appropriate definite integral.Find the length of the arc in one period of the cycloid x= t-sint ,y= 1-cost. The value of t run from 0 to 2πLet C be the curve given by f(x) = cosh x for 0 ≤ x ≤ t, where t > 0. Show that the arc length of C is equal to the area bounded by C and the x-axis. Identify another curve on the interval 0 ≤ x ≤ t with this property.
- 3. Find the arc length of the function y = x2 + x - 2 on the interval [-2,1].Use Simpson's Rule with n=10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. (Round your answers to three decimal places.) y=xsin(x) 0≤x≤2πa) Set up the integral that represents the length of the arc on the graph of y=x^2 that corresponds to the domain interval [0, 4]. Do not evaluate this integral, just set it up. b) Estimate the length of the arc from part a, using the Distance Formula to compute the length of the line segment joining the endpoints of this arc. c) Use the Trapezoidal Rule, with n = 8, to produce a better estimate of length of the arc (and the Integral value) from part a). List your partition – and the valuations of the integrand – before assembling the estimate.