(4) The line segment x = sin’t, y = cost osts sts about the y-axis to...
Find the area of the surface generated by revolving x=t+w - 2 sts V2 about the y-axis. The surface area obtained by revolving the given curve around the y-axis is (Type an exact answer in terms of st.) 1.
2. Consider the line segment & the zz-plane given by cone C by rotating the line about the z-axis. fromz 0 to z4. We can then obtain a 2 (a) 4 pts Find a parametric representation r(u, v) for C, including bounds for u and v. (b) (4 pts Calculate and simplify r x rl (c) 3 pts Use a double integral to find the surface area of C
2. Consider the line segment & the zz-plane given by cone...
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5 x, 0%xs9 , about the x axis. Check your answer with the following geometry formula Find the lateral (side) surface area of the cone generated by revolving the line segment y Lateral surface area x base circumference x slant height Set up the integral that gives the surface area of the cone. S: (Type exact answers, using x as needed.) 5 The lateral surface area of the cone generated by revolving the line segment y x. 0sxs9, about...
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...
Find the area of the surface generated by revolving the curve y= 0sxs6, about the x-axis The area of the surface is (Type an exact answer, using t as needed.) n Enter your answer in the answer box
Find the area of the surface generated by revolving the curve y= 0sxs6, about the x-axis The area of the surface is (Type an exact answer, using t as needed.) n Enter your answer in the answer box
Find the surface area generated by rotating the given curve about the y-axis. x = 312, y = 2, osts 4
Find the area of the surface generated by revolving x = 214-y. ys about the y-axis. x=20/4- The area is (Simplify your answer. Type an exact answer, using it as needed.)
(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...
Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and (5,7) about a. the x-axis, b. the y-axis, c. the line x = 7, and d. the line y = 2.
Consider the area bound by the line y- xì and y x? where 0 SxS1. Find the volume line of rotation when this area is rotated about a) the x-axis, b) the y-axis, c) the line
Consider the area bound by the line y- xì and y x? where 0 SxS1. Find the volume line of rotation when this area is rotated about a) the x-axis, b) the y-axis, c) the line