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21. Find the volume of the solid that is generated when the given region is revolved as described. The region bounded by f(x) = e

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21. Find the volume of the solid that is generated when the given region is revolved as described. The region bounded by f(x) = e" and the x-axis on [0, In 15] is revolved about the line x = In 15. The volume is (Type an exact answer.) Let R be the region bounded by y = sin x and the x-axis on the interval [0,]. Which is greater, the volume of the solid generated when R is revolved about the y-axis or the volume of the solid generated when R is revolved about the x-axis? The volume of the solid generated when R is revolved about the y-axis is (Type an exact answer.) The volume of the solid generated when R is revolved about the x-axis is (Type an exact answer.) Which is greater, the volume of the solid generated when R is revolved about the y-axis or the volume of the solid generated when R is revolved about the x-axis? O y-axis O X-axis24. Consider the function f(x) = 2 (4 +x2) -1/2 and the region R on the interval 0, $ ]. See the figure to the right. 1.2- a. Find the area of R. b. Find the volume of the solid generated when R is revolved about the x-axis. 0.6- c. Find the volume of the solid generated when R is revolved about the y-axis. R N- a. The area of R is square units. (Type an exact answer.) b. The volume of the solid generated when R is revolved about the x-axis is cubic units. Type an exact answer in terms of It.) c. The volume of the solid generated when R is revolved about the y-axis is cubic units. (Type an exact answer in terms of it.)

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