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Riemann sums are one method you can use to approximate the area under a curve, or approximate the integral. Instead of evaluating the integral directly, which we may not know how to do, we can instead divide the area into a set of rectangles, and then find the area of each rectangle, summing the areas together at the end to get an approximation of total area.
When you calculate the area using a Riemann sum, you can use the left endpoints of the rectangles, the right endpoints of the rectangles, or the midpoints of the rectangles. In this example, we'll use left endpoints.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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Tagged under: approximating area,riemann sums,left points,left endpoints,integrals,educational, ,approximation,calculus,Krista King,area curve,expert
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