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How to Integrate Sum Paper For Free

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Weve done several videos already where were approximating the area under a curve by breaking up that area into rectangles and then finding the sum of the areas of those rectangles as an approximation. And this was actually the first example that we looked at where each of the rectangles had an equal width. So we equally partitioned the interval between our two boundaries between a and b. And the height of the rectangle was the function evaluated at the left endpoint of each rectangle. And we wanted to generalize it and write it in sigma notation. It looked something like this. And this was one case. Later on, we looked at a situation where you define the height by the function value at the right endpoint or at the midpoint. And then we even constructed trapezoids. And these are all particular instances of Riemann sums. So this right over here is a Riemann sum. And when people talk about Riemann sums, theyre talking about the more general notion. You dont have to just do it this wa

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