ap-calculus-ab 2001 Q4

ap-calculus-ab · USA · free-response_formB Areas Between Curves Multi-Part Free Response with Area, Volume, and Additional Calculus

a) $f ( x ) = a ( x )$
$x ^ { 2 } = 2 ^ { x }$
$x ^ { 2 } - 2 ^ { x } = 0$
Using G. D. C.
(-0,767,0)
$( 2,0 )$
$( 4,0 )$
b) $\int _ { - 0.167 } ^ { 2 } \left( 2 ^ { x } - x ^ { 2 } \right) d x + \int _ { 2 } ^ { 4 } \left( x ^ { 2 } - 2 ^ { x } \right) d x$
C) $R ( x ) = 5 - y _ { 2 } = 5 - x ^ { 2 }$
$r | x | = 5 - 4 i = 5 - 2 ^ { x }$
volume $= \pi \int _ { - 0.767 } ^ { 2 } \left[ \left( 5 - x ^ { 2 } \right) ^ { 2 } - \left( 5 - x ^ { 2 } \right) ^ { 2 } \right] d x$

a) $f ( x ) = a ( x )$

$x ^ { 2 } = 2 ^ { x }$

$x ^ { 2 } - 2 ^ { x } = 0$

Using G. D. C.

(-0,767,0)

$( 2,0 )$

$( 4,0 )$

b) $\int _ { - 0.167 } ^ { 2 } \left( 2 ^ { x } - x ^ { 2 } \right) d x + \int _ { 2 } ^ { 4 } \left( x ^ { 2 } - 2 ^ { x } \right) d x$

C) $R ( x ) = 5 - y _ { 2 } = 5 - x ^ { 2 }$

$r | x | = 5 - 4 i = 5 - 2 ^ { x }$

volume $= \pi \int _ { - 0.767 } ^ { 2 } \left[ \left( 5 - x ^ { 2 } \right) ^ { 2 } - \left( 5 - x ^ { 2 } \right) ^ { 2 } \right] d x$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6