Apps. and Interpretation for IBDP Maths Ebook 1 | Page 226

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 64
�8
3
1. Consider the integral � d
11
x 12 x . The value of this integral is estimated by
�
�
trapezoidal rule with 4 trapeziums, such that the width of each trapezium is 0.75.
(a) Find an estimate of
�8
3
� d
11
x 12 x .
�
�
�8
3
It is given that the exact value of � d
11
x 12 x is 6.
�
�
[3]
(b)
Calculate the percentage error in the estimate.
[2]
2. Consider the integral
with 5 trapeziums.
�
3
4 e
x d x. The value of this integral is estimated by trapezoidal rule
0
(a)
(b)
Write down the width of each trapezium.
Hence, find an estimate of
It is given that the exact value of
3
� 4e
x d x.
0
3
� 4e
x d x is
0
3
4( e � 1) .
[1]
[3]
(c)
Calculate the percentage error in the estimate.
[2]
3. The following table shows the functional values of f( x ) from x � 5 to x � 6 :
x 5 5.125 5.25 5.375 5.5 5.625 5.75 5.875 6
f( x ) 8 7 6 5 4 3 f (5.75) f (5.875) 8
It is given that f (5.625) , f (5.75) , f (5.875) and f (6) forms an arithmetic sequence.
(a) (i) Write down the common difference of the an arithmetic sequence.
(b)
(ii) Hence, write down the exact values of f (5.75) and f (5.875) .
Find an estimate of
5
6
� f ( x )dx
.
[3]
[3]
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