Talk:Integral

Totality vs size

"Totality" might be better because integrals also describe such concepts as mass. But it's really hard to come up with a formulation that is both easy to grasp and accurate. Fredrik Johansson 13:54, 29 April 2007 (CDT)

I agree. "size" is not necessarily the best. Change it back to "totality" if you like. There may be something better. "Extent in space" doesn't cover all cases, either: one might want to integrate prices or interest rates or temperatures or something else, but since it says "intuitively" I think "extent in space" is good enough for that part -- it helps the reader get an image in their mind. I'll try to think of other words. --Catherine Woodgold 14:03, 29 April 2007 (CDT)

"Intuitively, we can think of an integral as a measure of the totality of an object with an extent in space. "

"... as a measure of the totality of some aspect, such as area or volume, of an object with an extent in space."

"... as a measure of some additive quality of an object."

"... as a measure of qualities such as area or volume, of the type whose values add when two objects are joined into a larger object."

"... as a measure of such qualities as area and volume."

"... as a way of extending the definition and measurement of area and volume to curved objects."

OK, I give up: leave it as "totality". I changed it back to the original. --Catherine Woodgold 18:35, 29 April 2007 (CDT)

Maybe you should just note that integrals generalize sums to (possibly) continuously varying quantities. Greg Woodhouse 13:47, 30 April 2007 (CDT)

The first sentence could be "An integral generalizes the idea of a sum to cover quantities which may be continuously varying, allowing for example the area or volume of curved objects to be calculated." --Catherine Woodgold 18:51, 30 April 2007 (CDT)