Analysis and Approaches for IBDP Maths Ebook 2 | Page 178

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 54
1. Use the substitution x � 10sec�
to show that
C is a constant.
�
1 1 x
dx�
arcsec �C, where
2
x x �100
10 10
[5]
2. Use the substitution x � sin�
, find the value of k such that
1
2
2
� 1
2
2
dx
� ,
k
0
1�
x
�
k � .
[6]
3. (a) Express
(b) Hence, show that
4. (a) Express
(b) Hence, show that
2
� � � in the form
x
x
2
2x
8
3 2
� 1
2
3 2
� �1
2
2 x
k ( x h)
1
d
2 8 x �
� � .
� � x�
2
�8x� 20 in the form
2
� � , where h , k � .
2
a( x h)
k
�2
1 � 1
� dx
� � .
�4
2 2
( x �8x�20) 64 32
� � , where a , h , k � .
[2]
[5]
[2]
[6]
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