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Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined by y=e" between y-1 and y-e. (a.) Set up, but do NOT evaluate, an integral with respect to y for the arc length of C. (b.) Set up, but do NOT evaluate, an integral with respect to x for the arc length of C. Set up, but do NOT evaluate, an integral for the area of the surface obtained by rotating C about the...
(10 marks) Let C be the curve 64x – - y3 = 0 between y = 0 and y = 3. Sketch the graph of this curve. In each part, set up, but do not evaluate, an integral or a sum of integrals that solves the problem. (a) Find the area of the surface generated by revolving C about the x-axis by integrating with respect to x. (b) Find the area of the surface generated by revolving C about the...
3. (6 points) Consider the curve y = 2 - 2.22 restricted to the first quadrant. (a) Set up a definite integral that gives the length of this curve. Do NOT evaluate the integral (b) Set up a definite integral that gives the surface area of the solid generated by rotating the curve about the x-axis. Do NOT evaluate the integral.
a. Set up an integral for the area of the surface generated by revolving the curve x = 3 sin y, 0 sys about the y-axis. b. Graph the curve. c. Use technology to find the surface area numerically. a. Set up an integral for the area of the surface generated by revolving the curve x = 3 sin y, 0 sys about the y-axis. b. Graph the curve. c. Use technology to find the surface area numerically.
14 1. (10 marks) Let C be the curve 27x - y = 0 between y=0 and y=4. Sketch the graph of this curve. In each part, set up, but do not ovaluate, an integral or a sum of integrals that solves the problem. (a) Find the area of the surface generated by revolving C about the x-axis by integrating with respect to x (6) Find the area of the surface generated by revolving C about the y-axis by integrating...
please help! I cannot figure this out. The graph below is of the curve defined parametrically by: x-sin t and y- sin 2t -0 5 0.5 -1 (a) SET UP THE INTEGRAL TO FIND THE AREA OF THE REGION ENCLOSED BY THE CURVE AND EVALUATE (b) SET UP THE INTEGRAL TO FIND THE LENGTH OF THE CURVE TRAVERSED EXACTLY ONCE. DO NOT EVALUATE. SIMPLIFY TO JUST BEFORE MAKING A SUBSTITUION. (c) SET UP THE INTEGRAL TO FIND THE TOTAL DISTANCE...
8. Use the shell method to set up and evaluate the integral y- 3x that gives the volume of the solid generated by revolving the plane region about the y-axis. a. 192R b. 384x C. 192x d. 384x e. 96x 7 9. Set up and evaluate the definite integral for the area of the surface formed by revolving graph of y-9-2 about the y-axis. Round your answer to three decimal places. 8. Use the shell method to set up and...
for b. y= sin(x^2-3x+1) og t par Set up, but do not evaluate, the integral required to compute the arc length of the curve cotr. y= 217from 0<x< /2. mense metied to compute Set up, but do not evaluate, the integral required to compute the surface area of the solid obtained by rotating the curve y=sin(x2 3x + 1), 0<x< 1 about the z-axis.
0. Using Let R be a region bounded by y = x?, y = 16 and x = SHELL METHOD, set up an integral to find the volume of the solid generated by revolving R around the line x 8. YOU DON'T NEED TO SOLVE THE INTEGRAL.
3. Suppose the curve x = = t3 – 9t, y=t+ 3 for 1 <t< 2 is rotated about the x-axis. Set up (but do not evaluate) the integral for the surface area that is generated.