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AP Central is the official online home for the AP Program and PreAP: apcentral.collegeboard.com. AP® CALCULUS AB
2005 SCORING GUIDELINES (Form B)
Question 1
Let f and g be the functions given by f ( x ) = 1 + sin ( 2 x ) and g ( x ) = e x 2 . Let R be the shaded region in the first quadrant enclosed by
the graphs of f and g 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
xaxis.
(c) The region R is the base of a solid. For this solid, the cross sections
perpendicular to the xaxis are semicircles with diameters extending
from y = f ( x ) to y = g ( x ) . Find the volume of this solid. The graphs of f and g intersect in the first quadrant at
( S , T ) = (1.13569, 1.76446 ) . S ∫0 ( f ( x ) − g ( x ) ) dx
S
= ∫ (1 + sin ( 2 x ) − e x 2 ) dx
0 (a) Area = 1 : correct limits in an integral in (a), (b),
or (c) ⎧ 1 : integrand
2: ⎨
⎩ 1 : answer = 0.429 (b) Volume = π ∫0 ( ( f ( x ) )
S ⎮
= π⌠ S ⌡0 2 ) − ( g ( x ) )2 dx ((1 + sin ( 2x )) 2 ( − ex ) 22 ⎧ 2 : integrand
⎪
−1 each error
⎪
⎪
Note: 0 2 if integral not of form
3: ⎨
b
⎪
c ∫ R 2 ( x ) − r 2 ( x ) dx
a
⎪
⎪ 1 : answer
⎩ ) dx ( = 4.266 or 4.267 ) S 2
⌠ π ⎛ f ( x) − g( x) ⎞
(c) Volume = ⎮
⎜
⎟ dx
2
⎠
⌡0 2 ⎝
S ⎧ 2 : integrand
3: ⎨
⎩ 1 : answer 2 ⌠ π ⎛ 1 + sin ( 2 x ) − e x 2 ⎞
=⎮
⎟ dx
2⎜
2
⎠
⌡0 ⎝
= 0.077 or 0.078 Copyright © 2005 by College Board. All rights reserved.
Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 2 AP® CALCULUS AB
2005 SCORING GUIDELINES (Form B)
Question 2 A water tank at Camp Newton holds 1200 gallons of water at time t = 0....
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This note was uploaded on 10/01/2009 for the course OC 9876 taught by Professor Dq during the Spring '09 term at UC Merced.
 Spring '09
 Dq

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