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If I start with an integral as the area under a curve.
And imagine that I colour it in with straight lines.
Then sum these lines.
Is this a useful way of visualising integrals?
i.e. converting 2 dimensions into 1.

Can anyone use this concept in any other integral questions?
(e.g. integrals involving trig functions, or e etc.)

(I know the word line is sloppily used here).

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If it's useful to you, then it's useful. –  Gerry Myerson Dec 7 '12 at 4:57
I would have said that if it hadn't been said. –  copper.hat Dec 7 '12 at 5:03
I would think of the line as a collection of tiles instead, each of which has area. –  copper.hat Dec 7 '12 at 5:04
It can be a useful way to look at things. a little treacherous. The idea goes back to Torricelli and Cavalieri, a bit before the official discovery of the calculus, and in some ways, to Archimedes. So you are in wonderful company. –  André Nicolas Dec 7 '12 at 5:10

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