# Trapezium rule

The trapezium rule is a method of finding the approximate value of the value of an integral between certain limits. In other words the trapezium rule is a way of calculating the area under the curve on a graph. You must know that an integration gives the area under a curve on a graph. The following is the trapezium rule.

Area = h/2(y

_{0}+ y_{n}+ 2(y_{1}+ y_{2}+ ... + y_{n-1}))h ⇒ interval between the x values (height of the trapeziums)

y ⇒ the y value at the end of each strip

The trapezium rule takes advantage of the are of a trapezium formula:

Area of trapezium = h(a + b)/2

## Trapezium rule Examples

Find the area between the x-axis and the curve y = x^{2} + 2 between x = 1 and x = 5 using the trapezium rule with 4 strips./

Answer

ExplanationFirst let’s draw a table to find out the y values.

So now we can use the trapezium rule. The trapezium rule states that as above:The The answer for the area between the curve of y = x

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | 3 | 6 | 11 | 18 | 27 |

Area = h/2(y

_{0}+ y_{4}+ 2(y_{1}+ y_{2}+ y_{3}))**h**is the height of the trapeziums or very simply the intervals between the**x**values. In the above table we have**x**values ranging from:**1, 2, 3, 4, and 5**The distance between these values is**1**Area = 1/2(3 + 27 + 2(6 + 11 + 18))

= 50 square units

^{2}+ 2 is**50 square units** LINK TO PAGE

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wow, this is great and easie

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Thanks, I am glad you found it easy. I have just added a few missing details that I forgot to add. I hope you understood everything.

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this ti the first time i come across Trapezium unfortunately i still do not understand the process

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Thank u.. Finally I got the trapezium rule.. The explanation was straight to the point..

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