The wiki states that:
"In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total."
This is untrue. The integral on its 'own' is an average. It is in fact exactly equal to the mean value of some primitive function f, provided f exists. However, an area is a product of two averages. Similarly, a volume is a product of three averages.
The general formula for area is: Average length of horizontal lines * Average length of vertical lines. Volume is: area * average length of lines perpendicular to plane of area.
The following link has more information:
220.127.116.11 17:04, 15 March 2009 (UTC)