MATHEMATICS 



13 



Simpson's Rule. The base line must be divided into an 

 even number of equal parts. The area is then equal to 



A = (a+n+42/*2+22/ts)-, 

 3 



in which a+n is the sum of the end ordinates; 42fo is four 

 times the sum of all intermediate even-numbered ordinates; 



and 22As is twice the 

 sum of all intermediate 

 odd -numbered ordi- 

 nates. This rule is 

 more accurate than the 

 trapezoidal rule. 



^r 



^-> 



EXAMPLE. Referring 

 to the preceding exam- 

 ple, what is the area ABCD according to Simpson's rule? 

 SOLUTION. A = [19+23+4(18+12 + 17) +2(14 + 13)] X ^3 

 = 4,733 sq. 1L 



AREA BOUNDED BY AN IRREGULAR CURVE 



Suppose that it is required to find the area enclosed by the 

 heavy irregular curve shown in the accompanying illustration. 



JP 



A broken line AEFMCHIA is drawn around the curved 

 boundary line and as close to it as convenient. Ordinates 

 to the straight lines thus drawn are measured from the points 



