Page 83 - statbility for masters and mates

Equating coef®cients:
Simpson's Rules for areas and centroids 71
A B C D 3h B 2C 3D 92 h B 4C 9D 9h
B 8C 27D 81 h 4
From which:
;Areaoffigure 38 hy1 98 hy2 98 hy3 38 hy4
A 38 h,B 98 h,C 98 h,andD 38 h Areaoffigure 38 h y1 3y2 3y3 y4
A coef®cient of 38 with multipliers of 1, 3, 3, 1 etc.
Simpson's Third Rule
In Figure 10.3:
Area of the elementary strip ydx
Let the area between y1 and y2 Ay1 By2 Cy3
or
This is Simpson's Second Rule.
Summary:
Area between y1 and y2 in figure
a0h 12a1h2 13a2h3
h O
ydx
Fig. 10.3