49
Paper 1 – Area Under a Curve
11
Example
Consider the graph of f ( x) �2sin 2x � 1, where 0 �x � � .
( a ) Find the x -intercept( s ) of f( x ) in 0 �x � � .
( b ) Hence , find the area of the region enclosed by the graph of f and the x -axis .
[ 2 ]
[ 2 ]
Solution
( a ) |
By considering the graph of y�2sin 2x� 1, |
|
x � 0.2617994 or x � 1.3089969
.
|
( M1 ) for valid approach |
Thus , the x -intercepts are 0.262 and 1.31 . |
A1 |
( b ) |
The area of the region |
1.3089969
� � 2sin 2x�1 dx ( A1 ) for correct approach
0.2617994
� 0.6848532654 � 0.685
A1
[ 2 ]
[ 2 ]
Exercise 49
1 . Consider the graph of f ( x) �� cos�
x , where 0�x
� 2.
( a ) |
Find the x -intercept( s ) of f( x ) in
0�x �
2.
|
( b ) |
Hence , find the area of the region enclosed by the graph of f and the x -axis. |
[ 2 ]
[ 2 ]
2 . Consider the graph of
f y
1
( ) e y�
1 � � , where 0� y � 2.
( a ) Find the y -intercept( s ) of f( y ) in 0� y � 2.
[ 2 ] ( b ) Hence , find the area of the region enclosed by the graph of f and the coordinate
axes . www . seprodstore . com
[ 2 ]
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