(b) use the shell method and integrate with respect to y. 53-62. Choose your method Let R be the region bounded by the Jollowing curves. Use the method of your choice to find the volume of the solid generated when R is revolved about the given axis 53. y-x-x", y = 0; about the x-axis. 54. y x y0; about the y-axis. 55. y x2 and y 2 - x2; about the x-axis 56. y sin x r and y = 1-sin x, for π/6 s 5m/6; about the x s x-axis 57. y--х, y 2x 2, x 2, and x 6; about the y-axis 58. y 3 y 0, and x 2; about the x-axi T59. y VInx,y VIn x2, and y 1; about the x-axis 60. y = 2, y = 2x + 2, and x = 6; about the y-axis 61 y = x2, y = 2-x, and x = 0, in the first quadrant, about the y-axis

Question

#54

(b) use the shell method and integrate with respect to y.
53-62. Choose your method Let R be the region bounded by the
Jollowing curves. Use the method of your choice to find the volume of
the solid generated when R is revolved about the given axis
53. y-x-x", y = 0; about the x-axis.
54. y x y0; about the y-axis.
55. y x2 and y 2 - x2; about the x-axis
56. y sin x
r and y = 1-sin x, for π/6 s
5m/6; about the
x s
x-axis
57.
y--х, y
2x
2, x
2, and x
6; about the y-axis
58. y 3 y 0, and x 2; about the x-axi
T59. y VInx,y VIn x2, and y 1; about the x-axis
60. y = 2, y = 2x + 2, and x = 6; about the y-axis
61 y = x2, y = 2-x, and x = 0, in the first quadrant, about
the y-axis
Expand
Transcribed Image Text

(b) use the shell method and integrate with respect to y. 53-62. Choose your method Let R be the region bounded by the Jollowing curves. Use the method of your choice to find the volume of the solid generated when R is revolved about the given axis 53. y-x-x", y = 0; about the x-axis. 54. y x y0; about the y-axis. 55. y x2 and y 2 - x2; about the x-axis 56. y sin x r and y = 1-sin x, for π/6 s 5m/6; about the x s x-axis 57. y--х, y 2x 2, x 2, and x 6; about the y-axis 58. y 3 y 0, and x 2; about the x-axi T59. y VInx,y VIn x2, and y 1; about the x-axis 60. y = 2, y = 2x + 2, and x = 6; about the y-axis 61 y = x2, y = 2-x, and x = 0, in the first quadrant, about the y-axis

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