Analysis and Approaches for IBDP Maths Ebook 1 | Page 198

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 67
4x
1. Consider the graph of f( x)
�
2
x � 1
, where f( x) � 0 for 0 � x � 3 . Let R be the region
enclosed by the graph of f , the x -axis and the line x � 3. Find the area of R .
[6]
2x
2. Consider the graph of f ( x) �e
� 1, for 0 �x
� ln 2. Let R be the region enclosed by the
graph of f , the x -axis and the line x � ln 2 . Find the area of R .
[6]
�
3. Consider the graph of g( x) � cos2x
, for 0 � x� k � . Let R be the region enclosed by
4
3
the graph of g , the x -axis and the line x�
k. If the area of R is
4 , find k . [6]
4. Consider the graph of g( x) � sin�
x , for 0� k � x� 1. Let R be the region enclosed by
the graph of g , the x -axis, the line x
k .
� k and the line x � 1. If the area of R is
1
2� , find
[6]
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