Analysis and Approaches for IBDP Maths Ebook 1 | Página 190

Your Practice Set – Analysis and Approaches for IBDP Mathematics
64
Paper 1 Section A – Finding the original
function with given derivative
Example
4x
Let f�( x)
�
2 6
(2x
�1)
. Given that
6
f (0) �� , find f( x ).
5
[6]
Solution
4x
f ( x) � d
(2x
�1)
� x
(M1) for indefinite integral
2 6
2
Let u�2x
� 1. A1
du
4x du 4xdx
dx � � �
� f( x)
1
� � 6 du
u
1 5
5 u �
� �
�
C
1
� � � C
A1
2 5
5(2x
�1)
6 1
� � � � C
M1
2 5
5 5(2(0) �1)
6 1
� � � � 1
5 5 C � C � � (A1) for correct value
1
� f( x) � � �1
A1 N4
2 5
5(2x
�1)
[6]
Exercise 64
1. Let
2. Let
3. Let
4. Let
2 3 6
�( ) �3 ( � 1) . Given that ( 1) 2
f x x x
2
�( ) � 2 sin( ) . Given that (0) 1
f x x x
3
f ( x) cos 2xsin 2x
f � � , find f( x ).
f �� , find f( x ).
��
�
� � . Given that f � � � 3
� 2 �
4
3 x
�( ) � 4 . Given that
f x x e
f
16
(2) e 1
, find f( x ).
� � , find f( x ).
[6]
[6]
[7]
[7]
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