Analysis and Approaches for IBDP Maths Ebook 2 | Page 194

Your Practice Set – Analysis and Approaches for IBDP Mathematics
59
Paper 2 Section A – More About Volumes
Example
The graph of
g x
2 5
( ) e ( e x�
1)
x
� � is obtained from the graph of f ( x)
� e by a translation
of p units in the direction of the x -axis followed by a translation of q units in the
direction of the y -axis.
(a) Find the values of p and q .
[4]
(b) The region bounced by the graph of g x
2 5
( ) e ( e x�
1)
� � , the x -axis and the lines
x � 1 and x � 3, is rotated through 2π radians about the x -axis. Find the volume
generated.
[2]
Solution
(a)
(b)
g x
2 5
( ) �e ( e x�
� 1)
g( x)
e e
x�3 2
� � (M1) for valid approach
g( x) f ( x 3) e
2
� � � (M1) for valid approach
2
�p
� 3,
q� e
A2
The volume generated
1
3
� � �
�
2
( g( x)) d
x
3
2 x�5 2
� � ( e ( e �1)) dx
(A1) for correct approach
1
� 384.7359437
� 385
A1
[4]
[2]
184
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