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Suppose that we have the following data:

enter image description here

Which I suppose records the amount of entries into a raffle contest from 12am to 8am,

and I wanted to just randomly use trapazoidal approximation to find the area underneath the points that I plot which I have calculated it to be 10.6875.

My teacher told me that there was a meaning behind this number and I wasn't really sure. I initially believed that this was the actual amount of entries submitted but realized that it would be foolish as the data itself shows the amount of entries being submitted.

I was wondering what this integral means?

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So I was looking for answers, and I found this: What does the integral of position with respect to time mean?

The answers to that might interest you. In your case, E(t) is essentially the position function.

However, if it turns out that you misunderstood the problem, and E(t) is actually how many ballots are added in each hour, then E(t) is essentially a velocity function. In that case, the integral on any interval would be the displacement (net change in value) of the ballot counts.

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