Simpson's Rules. Rules for finding areas of plane figures bounded by a straight line, two perpendiculars and a parabolic curve. They include Simpson's First and Second Rules and the 'Five-Eight' Rule.
Simpson's Second Rule. Base line is divided into equal parts that are a multiple of 3, the number of ordinates being 3x+1. Assuming 9 equal parts (10 ordinates), area will be found by the sum of end ordinates, plus twice 4th and 7th ordinates, plus three times all other ordinates, multiplying the sum by 3/8 of the common interval.