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y- 12e, y- , 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 shel. 10 10 -05 15 -0.5 os 1.5 -s -10- 10 -15 -13 -10 -0.5 as 10 1.5 -10 1.0 Now we can say that the volume of the solid created by rotating the region under y- 12eand above the -axis between x- O andx-1 around the yaxis is 2erh d 12 a The integral 2r dy can be done with the substitutionum and du dx. With the substitution, we have 2 +C. Going

y- 12e, y- , 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 shel. 10 10 -05 15 -0.5 os 1.5 -s -10- 10 -15 -13 -10 -0.5 as 10 1.5 -10 1.0 Now we can say that the volume of the solid created by rotating the region under y- 12eand above the -axis between x- O andx-1 around the yaxis is 2erh d 12 a The integral 2r dy can be done with the substitutionum and du dx. With the substitution, we have 2 +C. Going

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 please show all parts.  I am veery confused it will help so much

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-x2 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 y 10 10 5 -0.5 0.5 1lo 1.5 -0.5 0.5 1,0 1.5 -5 - 10 -10 y y 10 -1.5 -1.0 3.5 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-x and above the x-axis between x = 0 and x = 1 around the y-axis is V = 2rrh dx dx. The integral 27 12xex dy can be done with the substitution u = and du = dx. With the substitution, we have 27 12xe -x² dx = e" du = + C. Going back to x, the volume of our solid is
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-x2 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 y 10 10 5 -0.5 0.5 1lo 1.5 -0.5 0.5 1,0 1.5 -5 - 10 -10 y y 10 -1.5 -1.0 3.5 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-x and above the x-axis between x = 0 and x = 1 around the y-axis is V = 2rrh dx dx. The integral 27 12xex dy can be done with the substitution u = and du = dx. With the substitution, we have 27 12xe -x² dx = e" du = + C. Going back to x, the volume of our solid is
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