Analysis and Approaches for IBDP Maths Ebook 2 | Page 174

Your Practice Set – Analysis and Approaches for IBDP Mathematics
53
Paper 2 Section A – Partial Fractions Problems
Example
1
Let f( x)
� 2
1 � 16x
,
1
x � .
4
(a) Express f( x ) in partial fractions.
(b) Hence, find � f ( x)dx
.
[4]
[2]
Solution
(a)
1
f( x)
�
(1 � 4 x)(1 � 4 x)
Let
1 A B
� � , where A and
(1 � 4 x)(1 � 4 x) 1� 4x 1�
4x
B are constants.
1 A(1 �4 x) B(1 �4 x)
�
�
(1 � 4 x)(1 � 4 x) (1 � 4 x)(1 � 4 x) (1 � 4 x)(1 � 4 x)
1 A� 4Ax � B � 4Bx
�
(1 � 4 x)(1 � 4 x) (1 � 4 x)(1 � 4 x)
M1
1 � ( �4A � 4 B) x � ( A� B)
A1
0 � �4A�
4B
B�
A
1� A�
B
�1 � A� A
A1
1�
2A
1
A �
2
1
�B
�
2
1 1 1
� � �
A1
(1 � 4 x)(1 � 4 x) 2(1 � 4 x) 2(1 � 4 x)
[4]
164
SE Production Limited