10 Let C be the portion of the curve y-sinx for 0SxS T. Write down an integral representing the area of the surface obtained by revolving C about the indicated line. (a) the x-axis (c) the line x-4 (e) the line y 1 (b) the y-axis (d) the line x--1 (f) the line y -1 10 Let C be the portion of the curve y-sinx for 0SxS T. Write down an integral representing the area of the surface obtained by...
(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...
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...
2. [This problem is intended to measure the ability of students to apply the definite integral to determine the area (CO 5). Score 25] Sketch the region under the curve y = 2vx and y = 3 - x in the first quadrant. Find the area of the region. Find the center of mass of the region. 3. [This problem is intended to measure the ability of students to integral to determine the volume of solids of revolution (CO 5)....
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...
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.
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...
4. The curve y = rs for 0 < | < 1 is rotated about the z-axis to form a solid of revolution. (a) Find the volume of this solid of revolution 5 marks b) Calculate the surface area of this solid of revolution, leaving your answer in the form of a 5 marks definite integral. (c) Determine in the form of an integral the arc length of this curve from the points at which r0 and r 1, Use...
Parfait Glassis a volume of revolution, revolving y = 3x^2 around y-axis y=6 } density = 0.2 oz/in3 5 4.a. Find the total weight of the contents of the parfait glass in ounces (oz). The glass is a volume of revolution created by revolving the curve y=3xaround the y-axis with all measurements in inches. The glass has 3 layers making the parfait: icecream, choco- late sauce and whipped cream with densities listed in ounces per cubic inch. Write an expression...
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.