Analysis and Approaches for IBDP Maths Ebook 1 | Página 191

Front Page
65
Paper 1 Section A – Rules of definite integration
Example
Let
(a)
(b)
6
� f ( x )dx � 8.
2
Show that
Find the value of
2
� 2 f ( x )d x �� 16 .
6
5 6
� ( f ( x ) � x )d x � ( f ( x ) � x )d x
2 � .
5
[2]
[5]
15
Solution
(a)
(b)
�
2
2 f ( x)dx
6
6
2
� 2 � f ( x)dx
A1
�
6
2
�
�2 �� f ( x)dx
A1
�2( � 1)(8)
�� 16
AG N0
[2]
5 6
� �
( f ( x) � x)d x � ( f ( x) � x)dx
2 5
6
� � ( f ( x) �x)dx
(A1) for combining integrals
2
�
6 6
� f ( x)dx � xdx
2 � (A1) for separating integrals
2
6
�1
2
8
2 x �
� � �
� �
�2
A1
�1 2 1 2�
� 8 ��
(6) � (2) �
�2 2 �
A1
�� 8
A1 N3
[5]
www.seprodstore.com
183