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Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about the y-axis. y- 12e, y- 0, Sketch the region and a typical shell, Rotating a vertical strip around the y-axis creates a cylinder with radius r Sketch the region and a typical shell, 10 -0.5 -0.5 -10 10 -1.5 -1.0 -1.5 -1.0 -0.5 1.5 1.0 1.0 e can say that the volume of the solid created by rotating the region under y - 12e and above the x-axis between x-0 and x-1 around the y-axis is v- [2em de The integral 2 / 12xe dx can be done with the substitution u= and du- 24 / 120 ae -- dx. With the substitution, we have + C. Going back to x, the volume of our solid is

Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about the y-axis. y- 12e, y- 0, Sketch the region and a typical shell, Rotating a vertical strip around the y-axis creates a cylinder with radius r Sketch the region and a typical shell, 10 -0.5 -0.5 -10 10 -1.5 -1.0 -1.5 -1.0 -0.5 1.5 1.0 1.0 e can say that the volume of the solid created by rotating the region under y - 12e and above the x-axis between x-0 and x-1 around the y-axis is v- [2em de The integral 2 / 12xe dx can be done with the substitution u= and du- 24 / 120 ae -- dx. With the substitution, we have + C. Going back to x, the volume of our solid is

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...
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Hello, can you solve every part please? I am very confused

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the y-axis. y = 12e-x? y = 0, X = 0, X = 1 Sketch the region and a typical shell. Rotating a vertical strip around the y-axis creates a cylinder with radius r = and height h = Sketch the region and a typical shell. y 10 10 5 -0.5 0.5 1,0 1.5 -0.5 0.5 1,0 1.5 -10 - 10 y y 10 5 X -1.5 -1.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.5 1.0 1.5 Now we can say that the volume of the solid created by rotating the region under y = 12e and above the x-axis between x = 0 and x = 1 around the y-axis is V = 2arh dx 2Ax dx. 12e Jo The integral 2R 12xe e-x² dy can be done with the substitution u = dx. With the substitution, we have 27 + C. Going back to x, the volume of our solid is and du = 12xe dx eu du =-
Transcribed Image Text:Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the y-axis. y = 12e-x? y = 0, X = 0, X = 1 Sketch the region and a typical shell. Rotating a vertical strip around the y-axis creates a cylinder with radius r = and height h = Sketch the region and a typical shell. y 10 10 5 -0.5 0.5 1,0 1.5 -0.5 0.5 1,0 1.5 -10 - 10 y y 10 5 X -1.5 -1.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.5 1.0 1.5 Now we can say that the volume of the solid created by rotating the region under y = 12e and above the x-axis between x = 0 and x = 1 around the y-axis is V = 2arh dx 2Ax dx. 12e Jo The integral 2R 12xe e-x² dy can be done with the substitution u = dx. With the substitution, we have 27 + C. Going back to x, the volume of our solid is and du = 12xe dx eu du =-
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