250 



PRACTICAL MATHEMATICS 



This gives the area of the first two strips in terms of the ordi- 

 nates y lt y z , and y 3 . Taking the other strips in pairs and treating 

 each pair in a similar manner, 



A! - g&i + 4?/ 2 + 1/3} 



y 7 } 



Hence total area 



- A x + A, + A, .- . .' + A w 



= |{A+4B+2C} 

 o 



where A = sum of the first and last ordinates 

 B = sum of the even ordinates 

 C = sum of the remaining odd ordinates. 



It should be noticed that as this rule has been obtained by 

 adding the strips in pairs, it can only be used when the figure is 

 divided into an even number of strips and then there must be 

 an odd number of ordinates. 



135. Simpson's Second Rule. There is no such general rule 

 that can be applied when the figure is divided into an odd number 



FIG. 77. 



of strips, for the nature of the rule must depend upon the number 

 of strips taken at a time. 



