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Riemann sums are a tool you can use to approximate the area under a curve. Before you learn how to evaluate an integral, using rectangles to approximate the shape of the curve, and then finding the area of the rectangles instead, is the best you can do.
Usually, using rectangles with midpoints gives the most accurate approximation, and using left endpoints or right endpoints gives a less accurate approximation.
In general, if the curve is decreasing as you move from left to right, then using left endpoints will give an overestimation, and using right endpoints will give an underestimation. On the other hand, if the curve is generally increasing as you move from left to right, then using left endpoints will give an underestimation, and using right endpoints will give an overestimation.
In this video, we're talking about how to determine the shape of a curve in order to say whether using left endpoints will give an over or underestimation, and whether using right endpoints will give an over or underestimation. Then we'll show how to find an over and underestimation of the area under the curve.
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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,Krista King,area curve,calculus,educational,underestimation,integrals,riemann sums,overestimation,integration,estimating area
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