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Riemann sums

It may seem complex, but there's a relatively easy way to approximate the area under a curve. Watch this video to learn how Riemann sums work.

In this step we will look at how to use Riemann sums to approximate definite integrals. We will also learn about the difference between left and right, midpoint and trapezoidal Riemann sums.

  • Areas under curves can be estimated with rectangles. Such estimations are called Riemann sums.
  • To make a Riemann sum, we must choose how we’re going to make our rectangles. One possible choice is to make our rectangles touch the curve with their top-left corners. This is called a left Riemann sum:
  • Another choice is to make our rectangles touch the curve with their top-right corners. This is a right Riemann sum.
  • Riemann sums are approximations of the area under a curve, so they will almost always be slightly more than the actual area (an overestimation) or slightly less than the actual area (an underestimation).
  • In general, the more subdivisions (i.e. rectangles) we use to approximate an area, the better the approximation.
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Applications of Calculus

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