Analysis and Approaches for IBDP Maths Ebook 2 | Page 189

The region bounded by the curve
2π radians about the x -axis.
y �23 � x , the line L and the y -axis is rotated through
(d)
Show that the volume of the solid generated is
1
ln3
2� �
�9 � 3
�
�
� � .
3ln 3
[8]
13
4. Consider the function f ( x) � k log
2
x , x � 0 , k � 0 .
(a)
(b)
Show that f is a one-to-one function.
Find the expression of
� 1 �
A��5, �
� 32 � is a point on the graph of 1
f � .
1
f � , giving the answer in terms of k .
[2]
[2]
(c) Find the value of k .
Let R be the region enclosed by the graph of f , the x -axis and the line
x
2
� .
e
[2]
(d) Find the area of R .
Let S be the region enclosed by the graph of f , the x -axis, the y -axis and the line
y
� b. It is given that the area of R is equal to the area of S .
[9]
(e)
Show that
b� � .
2
log
2( e 2)
[4]
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