Analysis and Approaches for IBDP Maths Ebook 1 | Page 189

63
Paper 1 Section A – Integration of reciprocal functions
Front Page
Example
Solution
Given that
4 3
� d ln
1
3x
2 x �
�
k , find the value of k .
[6]
15
�
1
4
3
d
3x � 2 x
4
�1 �
�
�
� 3ln(3 x � 2)
�3
�
�1
A2
� ln(3(4) � 2) �ln(3(1) � 2)
(M1) for substitution
� ln14 � ln 5
A1
14
� ln 5
(A1) for correct formula
14
�k
� A1 N3
5
[6]
Exercise 63
1. Given that
2. Given that
3. Given that
4. Given that
10 5
� d ln
3
5x
1 x �
�
k , find the value of k .
6 4
� d 2ln
0
4x
1 x �
�
k , find the value of k .
k 1
� dx
� ln 2 , find the value of k .
0
3x
� 4
k 1 k
� d x � ln , find the possible values of k .
0
9�
x 2
[6]
[6]
[6]
[7]
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