Algebraic Manipulation Worksheet Page 4
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511. (Calculator Permitted) (2000-AB 1) Let R be the region in the first quadrant enclosed by the graphs of
2 x
y e
,
y
x
, and the y-axis, as shown in the figure above.
1 cos
(a) Find the area of the region.
(b) Find the volume of the solid generated when the region R is revolved about the line
y .
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(c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a
semicircle. Find the volume of this solid.
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