Analysis and Approaches for IBDP Maths Ebook 1 | Seite 216

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(c)
�
a
f�
( x )d x�
2
1
f ( a) � f (1) � 2
R1
(ln a �3) �(ln1� 3) � 2
(M1) for substitution
ln a �ln1 � 2
ln a � 2
A1
2
a� e
A1 N3
[4]
Exercise 72
1. The following diagram shows the graphs of
for 0�x
� 6.
f x � � x � x � and
2
( ) 0.5 3 2
0.5x
g( x) � 2e � ,
(a) Let A be the area of the region enclosed by the curves of f and g .
(i) Write down the values of x such that f ( x) � g( x)
.
(ii) Calculate the value of A .
(b) Find the value of x for which the gradient of f is equal to the gradient of g .
(c) It is given that
a g x x e �
4
�
�( )d �2( �1)
, find a .
0
[6]
[5]
[4]
2. The following diagram shows the graphs of
��
�
g( x) � sin � x�
� 4 � , for 0�x
� 4.
2
f ( x) � 0.1x �0.24x
� 0.174 and
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