Your Practice Set – Applications and Interpretation for IBDP Mathematics
47
Paper 1 – Finding Original Functions
Example
4x
Let f�( x) �
2 6
( 2x
�1 )
.
( a ) Express f( x ) as an indefinite integral of x .
( b ) Using the substitution u� answer in terms of x .
It is given that
6 f ( 0 ) �� .
5
( c ) Find the expression of f( x ).
2
2x
1
� to integrate the integral in ( a ), giving the
[ 1 ]
[ 3 ]
[ 2 ]
Solution
4x
( a ) f ( x) � � dx
A1
2 6
( 2x
�1 )
( b ) |
2 Let u�2x
� 1.
|
du 4x du 4xdx dx |
A1
|
1 � f ( x) �� du
6 u
|
( A1 ) for substitution |
|
1
�5 f
( x) � u
�C
�5
1 f
( x)
� � 2
5 5 (
2x �1 )
|
�
C
|
A1 |
6 1 ( c ) � � � � C
2 5
5 5 ( 2 ( 0 ) �1 ) C �� 1
1 � f( x) � � �1
2 5
5 ( 2x
�1 )
( M1 ) for substitution
A1
[ 1 ]
[ 3 ]
[ 2 ]
170
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