Apps. and Interpretation for IBDP Maths Ebook 1 | Page 219

61
Paper 1 – Area Under a Curve
Example
Consider the graph of f ( x) � 2( x � 2)(8 � x)
, where f( x) � 0 for a �x � b . Let R be the
region enclosed by the graph of f and the x -axis.
(a) (i) Write down the values of a and b .
(ii) Write down the equation of the axis of symmetry of f( x ).
(b) (i) Write down the integral representing the area of R .
(ii) Hence, find the area of R .
[3]
[2]
16
Solution
(a) (i) a � 2 , b � 8
A2 N2
(b)
(ii) x � 5
A1 N1
(i)
8
� 2( x � 2)(8 �x
)d x
A1 N1
2
[3]
Exercise 61
(ii) 72 A1 N1
[2]
1. Consider the graph of
3 2
f ( x) � �x �16x �69x
� 90 for x � 3, where f( x) � 0 for
3 �x� p. Let R be the region enclosed by the graph of f and the x -axis.
(a) (i) Write down the value of p .
(ii) Write down the coordinates of the maximum point of f( x ).
(b) (i) Write down the integral representing the area of R .
(ii) Hence, find the exact value of the area of R .
[3]
[2]
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