Exercise 47
11
1 . Let
� � .
3 f ( x) cos 2xsin 2x
( a ) Express f( x ) as an indefinite integral of x .
( b ) Using the substitution u� cos2x to integrate the integral in ( a ), giving the answer in terms of x .
��
� It is given that f � � � 3.
� 2 �
( c ) Find the expression of f( x ).
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2 . Let f � x � x x .
2
( ) 2 sin ( )
( a ) Express f( x ) as an indefinite integral of x .
2
( b ) Using the substitution u� x to integrate the integral in ( a ), giving the answer in terms of x .
It is given that f ( 0 ) �� 1.
( c ) Find the expression of f( x ).
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3 . Let
2 3 6
� � � . f ( x) 3 x ( x 1 )
( a ) Express f( x ) as an indefinite integral of x . [ 1 ]
( b ) Using a suitable substitution to integrate the integral in ( a ), giving the answer in terms of x .
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It is given that f ( �1 ) � 2.
( c ) Find the expression of f( x ).
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