AP微积分2003真题

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Calculus BC

2003 Free-Response Questions

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2003 AP

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CALCULUS BC FREE-RESPONSE QUESTIONS

CALCULUS BC

SECTION II, Part A

Time—45 minutes

Number of problems—3

A graphing calculator is required for some problems or parts of problems.

1. Let R be the shaded region bounded by the graphs of

y=

as shown in the figure above.

(a) Find the area of R.

(b) Find the volume of the solid generated when R is revolved about the horizontal line

y=1.

(c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is

a rectangle whose height is 5 times the length of its base in region R. Find the volume of this solid.

x

and

y

=

e

−3

x

and the vertical line

x=1,

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2003 AP

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CALCULUS BC FREE-RESPONSE QUESTIONS

2. A particle starts at point A on the positive x-axis at time t=0 and travels along the curve from A to B to C

to D, as shown above. The coordinates of the particle’s position

x

(

t

)

,y

(

t

)

are differentiable functions of t,

dy

p

t

p

t

+

1dx

where

x