# Trapezium Rule

Used to work out the area under a curve.

- Created by: Hummi C
- Created on: 04-06-12 12:15

First 245 words of the document:

Trapezium Rule

Formula of area of a trapezium=½(a+b)h

The formula to work out the area under a curve is:

A=1/2(y0+y1)h+1/2(y1+y2)h+1/2(y2+y3)h...

Note: the small numbers show which line you are referring to, in the below

example, y0 is at x=0, y1 is at x=1.

Worked example

Divide into

sections,

usually

how many

will be

stated in

the

question.

In this

case, the

area has

been

divided

into 4 (line

1 is at

x=1, line 2

is at x=2,

line 3 is at

x=3 and line 4 is at x=4). You then draw the following table:

X Y Y

0 0 (y0 (minimum))

1 1 (y1)

2 4 (y2)

3 9 (y3)

4 16 (y4 (maximum))

16 (this is the ymaximum 14 (this is the sum of all

yminimum) the other y-values at

Call this y0 each line)

Call this ythe rest

Then we solve for h. To do this, use the formula

h=(b-a)/n (where b is the greatest x-value, a is the lowest x-value and n is the

number of lines).

So

h=(4-0)/4

h=1

Then using the formula I mentioned in red, it would be:

A=1/2(0+1)1+1/2(1+4)1...

Or just write:

A=1/2(y0+2ythe rest)h

So

A=1/2(16+2x14)1

=1/2(16+28)

=22

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