Analysis and Approaches for IBDP Maths Ebook 2 | Page 195

Exercise 59
1. The graph of
g( x) ln( 7)
3
� x � is obtained from the graph of f ( x) ln
� x by a translation
of p units in the direction of the x -axis followed by a vertical stretch of scale factor q .
(a) Find the values of p and q .
(b) The region bounced by the graph of
g( x) ln( x 7)
3
� � , the x -axis and the lines
x � 3�
and x � 10 , is rotated through 2π radians about the x -axis. Find the
volume generated.
[4]
[2]
13
2. The graph of gx� ( ) 2 x
x
is obtained from the graph of f( x) �8 � 5 by a horizontal
compression of scale factor p followed by a translation of q units in the direction of the
y -axis.
(a) Find the values of p and q .
(b) The region bounced by the graph of gx� ( ) 2 x , the y -axis, the x -axis and the
line x � � , is rotated through 2π radians about the x -axis. Find the volume
generated.
3. Find the volume of the solid formed when the region bounded by the graph of
y� sec�
x and the line y� e is rotated by 2π about the y -axis.
[4]
[2]
[6]
4. Find the volume of the solid formed when the region bounded by the graph of
and the line y
� e is rotated by 2π about the y -axis.
y�
e
4x
[5]
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