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The trapezium rule

Suppose we want to evaluate

We do not know the integration of this function.

We can approximate the answer by using numerical

integration. (Trapezium rule).

Area

f(1)

½

f(2)

The trapezium rule

Suppose we want to evaluate

We use two trapeziums

Area

0.267

The trapezium rule

Suppose we want to evaluate

We use four trapeziums

x

f(x)

0.5

1

1.25

0.3386

1.5

0.2286

1.75

0.1572

2

0.1111

Area

0.125(0.5 2(0.3386 0.2286 0.1572) 0.1111

Area

0.257

The trapezium rule formula

The trapezium rule with n intervals

Example Using the trapezium rule with five

ordinates, find an estimate for the area under

the curve y 2x2 3 between x 1 and x 3.

n

0

1

2

3

4

xn

1.5

2.0

2.5

3.0

1

yn

7.5

11

15.5

21

5

Area ?

0.251 21 2(7.5 11 15.5)

23.5 unit2

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