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# Worked example: finding a Riemann sum using a table

When we have a table of values of a function, we can use it to find a Riemann sum approximation of that function.

## Want to join the conversation?

• If a rectangle is under x axis , should I subtract its area instead of adding ? Why ?
• Yes, even though an area can never be negative you will always want the "Net Area." So, when you have your areas of the rectangles for this instance you would subtract any area that is found below the x-axis.
• What if we are asked to do this same example but with unequal divisions?
• I may be misunderstanding, but if you're talking about the distance between two adjacent x values being different, then the answer is you won't be asked that. As shown in previous videos, you set each Δx values equal to one another in order to approximate. In the unlikely case you are actually asked to evaluate with different Δx values, you would simply take each value of Δx and multiply it with its corresponding f(x) value and add them all together. For example, if you had a table that listed several x values such as 1, 3, 7 and 10 as well as their respective f(x) values, say, 6, 7, 3 and 5, you would take Δ of the first two values and multiply it by the left or right side, like this: (3-1)(6) if you're taking the left side or (3-1)(7) if you're taking the right. then you move on to the next, which would be (7-3)(7) [for left] or (7-3)(3) for the right, and so on and so forth. Once you have all values, you would add them together.

Sorry this is long, didn't want to underexplain.
• are upper values = right endpoint values & lower values = lefthand values?
• If your talking about in terms of the type of Riemann sum [left/right], yes then the lower values are the left side and upper values are the right side.
• What if we are asked to find the reimann sums without an interval?
• What would be the proper sigma notation for a riemann sum, like the example sal did here, for instance?
(1 vote)
• what if we are asked to do thissame examples but in diffrent
(1 vote)
• Different in what sense?
• What about unequal subdivisions? I'm confused about that. I understand the rest of the steps.
(1 vote)
• Riemann sum is just sum of rectangles. When you have rectangle of different length across the x-axis you have unequal subdivisions,