Apps. and Interpretation for IBDP Maths Ebook 2 | Page 345

44.4
( a )
1059
( b )
dw 72.5sin (
0.5t
5.2 ) dt
( c )
218
Exercise 45
45.1 ( a ) 5.01cm
( b )
( i )
2 2t cos t � t sin t
( ii )
1.08 s
( iii ) 45.2 ( a ) 5.65 cm
� 3.39 cms �2
( b )
( i )
1.57 s
( ii )
4cos t
� 4tsin t
( iii )
� 8.00 cms �2 45.3 ( a ) ( ) 1 t t
v t � � e cos ( e )
( b ) ( i ) 2.39 s
( ii ) 45.4 ( a ) 6.28 s
117 cms �2
( b ) ( i ) 8.64 s
Exercise 46 t
( ii ) e ( sin t � cos t)
( iii ) � 7990 cms �2
46.2
( a )
( i )
CD � 10sin�
, OD �
10cos�
( ii )
400sin
�cos�
( iii )
100� � 400sin � cos�
( b ) ( i )
2 2
400 ( sin cos )
� � ( ii ) � � 0.785 rad ( iii ) � � 0.785 rad
( iv )
114
( c )
� � �
0,
� �
2
46.3
( a )
t � 0 or t �
6
( b ) ( i )
�
Q� t � t � t �
2
( ) 3 24 36
( ii )
t � 2 or t �
6
( iii )
t �
2
( iv )
32
( c )
( i )
�
20
( ii )
t � 0, t �
6
46.4
( a )
t �
12
( b )
( i )
2 P�( t) � �3t
�18t �
24
( ii )
t � 2 or t �
4
( iii )
t �
2
( iv )
700
( c )
( i )
704
( ii )
720
( d )
3
46.1
( a )
( i )
� �
�
( ii )
P �
16sin�
( b )
( i )
dP
16cos� d�
( ii )
� �
1.57 rad
( iii ) � � 1.57 rad ( iv ) 16
( c ) � � 0, � � �
Chapter 11
Exercise 47
47.1 ( a ) ( b )
( c ) 47.2 ( a )

� �

1 ( ) cos
4 f x � � 2 x � C 8 1 4 25 f ( x) � � cos 2x �
8 8

2 f ( x) � � 2xsin ( x ) dx

3 f ( x) cos 2xsin 2xdx
Answers
( b ) ( c )
2 f ( x) � �cos ( x ) � f x
2
( ) �� cos ( x )
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