Exercise 51
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1 . The region R is enclosed by the x -axis , the graph of
6 y e 2 x � � � . y�e
2x
� 1 and the graph of
( a ) Write down the x -intercept of
( i ) y
2x � � ; e
1
( ii )
6 y e 2 x � � � , giving the answer in terms of e .
( b ) Write down the x -coordinate of the point of intersection of the graph of y�e
2x
� 1 and the graph of
( c ) Hence , find the area of R .
6 y e 2 x � � � .
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2 . The region R is enclosed by the x -axis , the graph of y� 2ln x and the graph of
4 y�8
� x.
2 e
( a ) Write down the x -intercept of
( i ) y� 2ln x;
4
( ii ) y�8
� x, giving the answer in terms of e .
2 e
( b ) Write down the x -coordinate of the point of intersection of the graph of 4 y� 2ln x and the graph of y�8
� x.
2 e
( c ) Hence , find the volume of the solid of revolution formed when R is rotated through 2π about the x -axis .
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