Before attempting this reading it would be a good idea to learn the

trapezium rule here, because I won't go so much into details about the logic behind. I will concentrate more on how to use the rule rather than how it works. Thomas Simpson (20 August 1710 – 14 May 1761) was a British mathematician, inventor and eponym of Simpson's rule to approximate definite integrals.
Suppose we wanted to find the area under the graph of

y = f(x) between

x = a and

x = b The graph for the problem is shown below.

We would usually integrate to find out the area for this so the area would be;

There might come a situation when we can't integrate the function in this case we do an approximation. The Simpson's rule is very logical. The following diagram shows a graph followed by the Simpson's rule.
[caption id="attachment_762" align="alignnone" width="598" caption="simpson rule"]

[/caption]

*...where h is the width of each strip and ***n** is the even number
The more strips involved or you have in the rule the better the approximation.

## Example

Use the Simpson's rule with 8 strips to calculate an approximation to the following integral:

First we need to work out the width of each strip to use for

**h** in the Simpon's rule. We know that the region we want to find the area for runs from

**x=-1** to

**x=3**, so the total width is a

**4**. That must mean that the width of each strip is

**4/8=0.5** So we now need to work out the

**y** values at each point. A good way of finding these values is by drawing a table as below.
For example: when

**x = -1**
This is how we find the x values.

-1 |
-0.5 |
0 |
0.5 |
1 |
1.5 |
2 |
2.5 |
3 |

-1 |
-0.5 |
0 |
0.5 |
1 |
1.5 |
2 |
2.5 |
3 |

So we now since we know the y values at each x point we can move on to using the Simpson's rule as the following;

And the answer for the area between the specified points is

**6.80**
This is how you use the Simpson's rule. It's that simple!
;

//Comments
Before attempting this reading it would be a good idea to learn the

trapezium rule here, because I won't go so much into details about the logic behind. I will concentrate more on how to use the rule rather than how it works. Thomas Simpson (20 August 1710 – 14 May 1761) was a British mathematician, inventor and eponym of Simpson's rule to approximate definite integrals.
Suppose we wanted to find the area under the graph of

y = f(x) between

x = a and

x = b The graph for the problem is shown below.

We would usually integrate to find out the area for this so the area would be;

There might come a situation when we can't integrate the function in this case we do an approximation. The Simpson's rule is very logical. The following diagram shows a graph followed by the Simpson's rule.
[caption id="attachment_762" align="alignnone" width="598" caption="simpson rule"]

[/caption]

*...where h is the width of each strip and ***n** is the even number
The more strips involved or you have in the rule the better the approximation.

## Example

Use the Simpson's rule with 8 strips to calculate an approximation to the following integral:

First we need to work out the width of each strip to use for

**h** in the Simpon's rule. We know that the region we want to find the area for runs from

**x=-1** to

**x=3**, so the total width is a

**4**. That must mean that the width of each strip is

**4/8=0.5** So we now need to work out the

**y** values at each point. A good way of finding these values is by drawing a table as below.
For example: when

**x = -1**
This is how we find the x values.

-1 |
-0.5 |
0 |
0.5 |
1 |
1.5 |
2 |
2.5 |
3 |

-1 |
-0.5 |
0 |
0.5 |
1 |
1.5 |
2 |
2.5 |
3 |

So we now since we know the y values at each x point we can move on to using the Simpson's rule as the following;

And the answer for the area between the specified points is

**6.80**
This is how you use the Simpson's rule. It's that simple!
;