Instructional Video

Approximating Area Using Rectangles

Finding area using rectangles—isn't that a little too simplistic for a calculus course? Viewers learn how to approximate area under a curve using rectangles in the first installment of a seven-part video series on the definite integral. The three problem videos cover examples of using the left-hand and right-hand sums to approximate area.

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Instructional Ideas
  • Challenge learners to come up with a rule for when the left-hand sums and right-hand sums are over- or underestimates
Classroom Considerations
  • Videos use LHS for left-hand sum and RHS for right-hand sum, which may not match what you use in the classroom
  • Problem Video Three uses a TI-84 calculator
  • Video models the process of approximating area step-by-step
  • Problem Video Three shows how using a greater number of rectangles results in more accurate approximation, leading to the concept of a definite integral as a limit of Riemann sums
  • If showing the entire series in one sitting, the website might require membership 
  • Videos only cover left- and right-hand sums (no midpoint or trapezoidal approximations)