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- Apr 10th 2008, 12:18 PMski4life912
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- Apr 10th 2008, 12:29 PMski4life912
Come to think of it maybe some kind of parabola or something where it changes direction and areas cancel out?

- Apr 10th 2008, 12:33 PMo_O
Did you type the question correctly or am I missing something (Thinking)? There are several functions which are continuous over [-1,2] with partitions of that same interval used to calculate the areas under them.

- Apr 10th 2008, 12:47 PMski4life912
Well right, the general question was do they exist? if so give an example if not why not, at first I didn't think they existed but now im just thinking of examples that fit that.

- Apr 10th 2008, 01:00 PMo_O
Any linear equation would work really. For example, consider over the interval [-1, 2].

Length of each subinterval:

Consider your partition with left sample points:

So your Riemann sum:

etc. etc.