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, Sketch the region and a typical shell. Step 1 Rotating a vertical strip around the y-axis creates a cylinder with radius r = O O -0.5 -0.5 y 10 -10 y 10 5 -5 -10 0.5 X = 1 0.5 1,0 1,0 1.5 1.5 X X -1.5 -1.0 -0.5 -1.5 and height h = -1.0 y 10 5 y 5 0.5 0.5 1.0 1.0 . Sketch the region ar 1.5 X 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 = 12e-x² 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 O -0.5 -0.5 y 10 -10 y 10 5 -5 -10 0.5 X = 1 0.5 1,0 1,0 1.5 1.5 X X -1.5 -1.0 -0.5 -1.5 and height h = -1.0 y 10 5 y 5 0.5 0.5 1.0 1.0 . Sketch the region ar 1.5 X 1.5 X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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,
Sketch the region and a typical shell.
Step 1
Rotating a vertical strip around the y-axis creates a cylinder with radius r =
O
O
-0.5
-0.5
y
10
-10
y
10
5
-5
-10
0.5
X = 1
0.5
1,0
1,0
1.5
1.5
X
X
-1.5 -1.0 -0.5
-1.5
and height h =
-1.0
y
10
5
y
5
0.5
0.5
1.0
1.0
. Sketch the region ar
1.5
X
1.5
X
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