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FIGURE 171283 /3bortio 9rgola aed OFor another method see Exercise 64.6.2 EXERCISES15. y x1-18 Find the volume of the solid obtained by rotating the regionbounded by the given curves about the specified line. Sketch theregion, the solid, and a typical disk or washer.16. xy = 1,17. x = y'1. yx+ 1, y = 0, x = 0, x = 2; about the x-axis18. y x,2. y 1/x, y = 0, x = 1, x = 4; about the x-axis3. y x1, y = 0, x= 5; about the x-axis19-30 Refee, y= 0, x = -1, x = 1; about the x-axis4. yrotating the5. x 2y, x = 0, y 9; about the y-axis0:6. 2x y, x = 0, y 4; about the y-axis7. y x, y= x, x > 0; about the x-axis6 x, y = 2; about the x-axis8. yx, x = 2y; about the y-axis9. y10. x 2 y, x= y; about the y-axis11. y x, x= y; about y = 11, x = 2; about y -312. y x, y19. R1 ab13. y 1sec x, y 3; about y 121. Ri ab14. y sin x, y = cos x, 0 < xTT/4; about y = -1

Question

#3

FIGURE 17
128
3 /3
bortio 9
r
gola aed O
For another method see Exercise 64.
6.2 EXERCISES
15. y x
1-18 Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified line. Sketch the
region, the solid, and a typical disk or washer.
16. xy = 1,
17. x = y'
1. y
x+ 1, y = 0, x = 0, x = 2; about the x-axis
18. y x,
2. y 1/x, y = 0, x = 1, x = 4; about the x-axis
3. y x1, y = 0, x= 5; about the x-axis
19-30 Refe
e, y= 0, x = -1, x = 1; about the x-axis
4. y
rotating the
5. x 2y, x = 0, y 9; about the y-axis
0:
6. 2x y, x = 0, y 4; about the y-axis
7. y x, y= x, x > 0; about the x-axis
6 x, y = 2; about the x-axis
8. y
x, x = 2y; about the y-axis
9. y
10. x 2 y, x= y; about the y-axis
11. y x, x= y; about y = 1
1, x = 2; about y -3
12. y x, y
19. R1 ab
13. y 1sec x, y 3; about y 1
21. Ri ab
14. y sin x, y = cos x, 0 < xTT/4; about y = -1
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FIGURE 17 128 3 /3 bortio 9 r gola aed O For another method see Exercise 64. 6.2 EXERCISES 15. y x 1-18 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. 16. xy = 1, 17. x = y' 1. y x+ 1, y = 0, x = 0, x = 2; about the x-axis 18. y x, 2. y 1/x, y = 0, x = 1, x = 4; about the x-axis 3. y x1, y = 0, x= 5; about the x-axis 19-30 Refe e, y= 0, x = -1, x = 1; about the x-axis 4. y rotating the 5. x 2y, x = 0, y 9; about the y-axis 0: 6. 2x y, x = 0, y 4; about the y-axis 7. y x, y= x, x > 0; about the x-axis 6 x, y = 2; about the x-axis 8. y x, x = 2y; about the y-axis 9. y 10. x 2 y, x= y; about the y-axis 11. y x, x= y; about y = 1 1, x = 2; about y -3 12. y x, y 19. R1 ab 13. y 1sec x, y 3; about y 1 21. Ri ab 14. y sin x, y = cos x, 0 < xTT/4; about y = -1

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Step 1

Formula used:

Volume for a solid generated by a curve (y) bounded by the x values of a and b, which revolves about the x- axis is

 

V =r[y'd*
a
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V =r[y'd* a

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Step 2

Given that

 

yvx-1
..(1)
...(2)
x 5about the xaxis
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yvx-1 ..(1) ...(2) x 5about the xaxis

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Step 3

Sketch the curve:

...

x= 5
y=V(x=1)
2
6
4
4
y = 0
-2
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x= 5 y=V(x=1) 2 6 4 4 y = 0 -2

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Tagged in

Math

Calculus

Integration

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