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 = 4e-x² y = 0, x = 0, x = 1 Sketch the region and a typical shell. Step 1 Rotating a vertical strip around the y-axis creates a cylinder with radius r = -1.5 -1.0 -0.5 O -0.5 y 4 -2 -4 y 3 2 1 0.5 0.5 1.0 1,0 1.5 1.5 X X -1.5 -1.0 -0.5 y 4 -4 and height h = -0 y 0.5 8.5 1.0 1,0 Sketch the region and a typical shell. X 1.5 1.5 X
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 = 4e-x² y = 0, x = 0, x = 1 Sketch the region and a typical shell. Step 1 Rotating a vertical strip around the y-axis creates a cylinder with radius r = -1.5 -1.0 -0.5 O -0.5 y 4 -2 -4 y 3 2 1 0.5 0.5 1.0 1,0 1.5 1.5 X X -1.5 -1.0 -0.5 y 4 -4 and height h = -0 y 0.5 8.5 1.0 1,0 Sketch the region and a typical shell. X 1.5 1.5 X
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 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...
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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 = 4e−x2, y = 0, x = 0, x = 1
Sketch the region and a typical shell.
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.
4e-x²,
X = 1
y = 4e
y = 0,
x = 0,
Sketch the region and a typical shell.
Step 1
Rotating a vertical strip around the y-axis creates a cylinder with radius r =
O
-1.5
-0.5
-1.0 -0.5
y
4
2
-2
y
3
2
1
0.5
0.5
1,0
1.0
1.5
1.5
X
X
-1.5 -1.0
-0.5
O
y
4
-4
and height h =
y
2
0.5
0.5
110
1.0
Sketch the region and a typical shell.
1.5
1.5
X
X
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