This is called the trapezium rule for width h (see figure 5.6).
P2 5
y y
x
Exercise 5C
y1
y
y
y2 y y
1
2
x
Figure 5.6
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Look at the three graphs in figure 5.7, and in each case state whether the trapezium rule would underestimate or overestimate the area, or whether you cannot tell. y
y
y
x
x
(i)
x
(ii)
(iii)
Figure 5.7
EXERCISE 5C
1
The speed v in ms 1 of a train is given at time t seconds in the following table. t
0
10
20
30
40
50
60
v
0
5.0
6.7
8.2
9.5
10.6
11.6
The distance that the train has travelled is given by the area under the graph of the speed (vertical axis) against time (horizontal axis). (i) (ii)
Estimate the distance the train travels in this 1-minute period. Give two reasons why your method cannot give a very accurate answer.
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