Apps. and Interpretation for IBDP Maths Ebook 1 | Page 223

63
Paper 1 – Trapezoidal Rule
Example
�
12 3
Consider the integral ( x)dx
. The value of this integral is estimated by trapezoidal
0
rule with 6 trapeziums.
(a)
(b)
Find the width of each trapezium.
Hence, find an estimate of
12 3
� ( x)dx
.
0
[2]
[3]
16
Solution
(a)
(b)
The width of each trapezium
12 � 0
� (A1) for correct substitution
6
� 2
A1 N2
[2]
The estimate of
�
12 3
( x)dx
0
1 (2) �3 0 3 12 2( 3 2 3 4 3 6 3 8 3 10)
�
2 �
� � � � � � �
�
(A2) for substitution
� 19.92718325
� 19.9
A1 N3
[3]
Exercise 63
1. Consider the integral
with 4 trapeziums.
�
1
7
x
0.3
dx. The value of this integral is estimated by trapezoidal rule
(a)
(b)
Find the width of each trapezium.
Hence, find an estimate of
7
0.3
� x dx.
1
[2]
[3]
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