J-4116x1(16 x2) dx330- .1283 /3or another method see Exercise 64.(Cootating the region15. y x, y0, x = 1; about x 2ine. Sketch the16. xy 1, y= ), x = 1, x = 2; about x = -117. x y2, x= 1 - y; about x 3he x-axis18. y x, y 0, x = 2, x = 4; about x = 1x-axisxis19-30 Refer to the figure and find the volume generated byrotating the given region about the specified line.x-axisbyAC(O, 1)RZB(1, 1)y=rTOWOXA(1, 0)19. Ri about OA20. R1 about 0C=-121. Ri about AB22. Ry about BC

Question
Asked Sep 9, 2019

#15

J-4
1
16x
1
(16 x2) dx
3
3
0
- .
128
3 /3
or another method see Exercise 64.
(Co
otating the region
15. y x, y0, x = 1; about x 2
ine. Sketch the
16. xy 1, y= ), x = 1, x = 2; about x = -1
17. x y2, x= 1 - y; about x 3
he x-axis
18. y x, y 0, x = 2, x = 4; about x = 1
x-axis
xis
19-30 Refer to the figure and find the volume generated by
rotating the given region about the specified line.
x-axis
b
yA
C(O, 1)
RZ
B(1, 1)
y=r
TOW
O
X
A(1, 0)
19. Ri about OA
20. R1 about 0C
=-1
21. Ri about AB
22. Ry about BC
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J-4 1 16x 1 (16 x2) dx 3 3 0 - . 128 3 /3 or another method see Exercise 64. (Co otating the region 15. y x, y0, x = 1; about x 2 ine. Sketch the 16. xy 1, y= ), x = 1, x = 2; about x = -1 17. x y2, x= 1 - y; about x 3 he x-axis 18. y x, y 0, x = 2, x = 4; about x = 1 x-axis xis 19-30 Refer to the figure and find the volume generated by rotating the given region about the specified line. x-axis b yA C(O, 1) RZ B(1, 1) y=r TOW O X A(1, 0) 19. Ri about OA 20. R1 about 0C =-1 21. Ri about AB 22. Ry about BC

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check_circleExpert Solution
Step 1

Given region which are bounded by the below curve and rotating about the line x=2 is

y x, y 0,x 1
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y x, y 0,x 1

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Step 2

For finding the volume of solid, observe that the shape of the figure looks like cylindrical shell after rotation and the volume of the cylindrical shell is given by

dV 2rhd
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dV 2rhd

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Step 3

y=x3 will work as height of the region being revolved about x=2. Since the...

3
=2-x
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3 =2-x

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