Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
In problems 11 – 12, use shells to find the volume of the solid obtained by rotating the given region
about the specified line. Sketch the region, the area to be rotated, and a typical rectangle.
6.
11.
y = -
y = \3x – 11
y = x – 3
у аxis
12.
x+2
y =x+
-1
7
x axis
expand button
Transcribed Image Text:In problems 11 – 12, use shells to find the volume of the solid obtained by rotating the given region about the specified line. Sketch the region, the area to be rotated, and a typical rectangle. 6. 11. y = - y = \3x – 11 y = x – 3 у аxis 12. x+2 y =x+ -1 7 x axis
13.
Set up the integral for finding the volume obtained by rotating the region between the curves
1
y = -x²
y = 4x – 6
using the specified method and the line of rotation.
y = x²
2.
a.
y = ÷x²
b.
y = 4x – 6
About y = -2
washers
X.
y =
= 4x – 6
%3D
About x = 9
washers
y = x²
y = x²
с.
d.
y = 4x – 6
About y = -2
shells
y = 4x – 6
About x = 9
-
shells
expand button
Transcribed Image Text:13. Set up the integral for finding the volume obtained by rotating the region between the curves 1 y = -x² y = 4x – 6 using the specified method and the line of rotation. y = x² 2. a. y = ÷x² b. y = 4x – 6 About y = -2 washers X. y = = 4x – 6 %3D About x = 9 washers y = x² y = x² с. d. y = 4x – 6 About y = -2 shells y = 4x – 6 About x = 9 - shells
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