Analysis and Approaches for IBDP Maths Ebook 2 | Page 181

55
Paper 1 Section A – Area Under a Curve
Example
�
Consider the graph of f ( x) � 2 tan 2x sec 2x
, where f( x) � 0 for 0 � x � . Let R be the
4
�
region enclosed by the graph of f , the x -axis and the line x � . Find the area of R .
6
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13
Solution
The area of R
�
6
0
� � f ( x)dx
(A1) for correct approach
�
6
0
� � 2tan 2 x sec2 x d x
Let u� 2x. (M1) for substitution
du
2 du
2dx
dx � � �
� �� � �
x� � u � 2�
��
6 � 6 � 3
x� 0 � u� 2(0) � 0
�
�
6
�
3
0 0
�� f ( x)dx � tan usecudu
(A2) for correct working
�
06 3
0
�
�
�
� f ( x)dx � secu
A1
�
6
0
�
�
6
0
�
�
6
0
�
f ( x)dx
�sec �sec0
3
f ( x)dx
�2 �1
� f ( x)dx
�1
A1
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