Let R be the region bounded by the following curves. Use the shell method to fin

Question

Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. y=2x^(-3/2), y=2, y=128 and x=0 Set up the integral that gives the volume of the solid. Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. y=2x^(-3/2), y=2, y=128 and x=0 Set up the integral that gives the volume of the solid. Set up the integral that gives the volume of the solid.

Explanation / Answer

y=2x^(-3/2)

y=2/x^(3/2)

x^(3/2) =2/y

x=(2/y)2/3

y=2x^(-3/2), y=2, y=128 and x=0

volume by shell method v = [2 to 128] 2 y f(y) dy

v = [2 to 128] 2 y (2/y)2/3 dy

v = [2 to 128] 2 y (2)2/3y-2/3 dy

v = (2)5/3 [2 to 128] y1/3 dy

v = (2)5/3[2 to 128] [(3/4)y4/3 +c]

v = (2)5/3 [(3/4)1284/3 +c -(3/4)24/3 -c]

v = (2)5/3 [(3/4)228/3 -(3/4)24/3 ]

v =3 (2)5/3 [222/3 -2-2/3 ]

v =3 [227/3 -23/3 ]

v =3 [29 -2 ]

v=1530

Using shell method the volume of the solid generated when R is revolved about the x-axis=1530

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