Analysis and Approaches for IBDP Maths Ebook 2 | Page 190

Your Practice Set – Analysis and Approaches for IBDP Mathematics
58
Paper 1 Section B – Areas Between Curves
Example
3
Consider the equation log3 y � log9 .
2
x
(a)
Express y in terms of x , giving the answer in the form
y
b
� , where a , b� .
[6]
Let f be the function found in (a). R is the region bounded by the graph of f , the lines
x
� e and x
� c where c
� e, and the x -axis. It is given that the area of R is 2 3.
ax
3
(b) Show that c� e .
The function g is formed by reflecting f about the x -axis.
[5]
(c)
(d)
Show that
Hence, find
6 �
� ( f ( x) � g( x))dx
� 2 3 ln 6 , where � � 0 .
�
1296
� ( f ( x ) � g ( x ))d x .
1
[4]
[4]
Solution
3
x
log9
y 3
� log9 (A1) for correct formula
2
log 3 x
(a) log3 y � log9 2
9
log9
y 3
� log9 2
1 x
(A1) for correct value
2
3
2log9 y � log9 2
x
(M1) for valid approach
2 3
log9 y � log9 2
x
(A1) for correct approach
2 3
�y
�
2
x
M1
y �
y
3
2
x
1
� 3x �
A1
[6]
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