# 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.

…where

**h**is the height of the trapeziums or the

**x**values interval. And the

**y**s values are the y values at the end of each strip as shown below.

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

The rule works by splitting the area under a curve into a number of trapeziums we could find the area for. For example consider the graph in the following diagram,

The area below the graph curve has been split into a number of trapeziums. These trapeziums have been noted by letters A, B, C, and D

## Example

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.

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

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

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

So now we can use the trapezium rule. The trapezium rule states that as above:

The **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**

The answer for the area between the curve of y = x^{2} + 2 is **50 square units**

And that’s how you work with the trapezium rule.

wow, this is great and easie

Like or Dislike: 9 10

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.

Like or Dislike: 9 9

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

Like or Dislike: 0 11

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

Like or Dislike: 4 3