Trapezium Rule

Used to work out the area under a curve.

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  • Created by: Hummi C
  • Created on: 04-06-12 12:15
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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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Therefore the area under the curve is roughly 22, however this is not accurate
because there are only 4 trapeziums: to increase accuracy, increase n (the
number of lines).…read more

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