Ws 6.6 Improper Integrals Worksheet Page 5
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7Calculus Maximus
WS 6.6: Improper Integrals
Free Response
2
.
x
12. (AP 1996-1) Consider the graph of the function h given by
h x
e
for 0
x
(a) Let R be the unbounded region in the first quadrant below the graph of h. Find the volume of
the solid generated when R is revolved about the y-axis.
(b) Let
A w be the area of the shaded rectangle shown in the figure. Show that
A w has its
maximum value when w is the x-coordinate of the point of inflection of the graph of h.
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