Error: Over and Underestimates from Left, Right, Midpoint, and Trapezoid Sums
In this video we discuss how to determine if you're left Riemann sum, right Riemann sum, Midpoint Riemann sum, or trapezoidal sum is giving an over or underestimate of the true value of a definite integral. I try to emphasize that drawing a couple of pictures will always answer the question for you! (Except for midpoints, which I think is way less obvious from a simple picture so I remember it just gives the opposite of whatever the trapezoidal sum would give. This is something you will very likely see on the AP Calculus AB or AP Calculus BC exam multiple choice or Free Response Questions (FRQs). The material comes from Unit 6 (specifically Unit 6.2 of the courses.)

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Left, Right, & Midpoint Riemann Sum Formulas

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Determining Over or Underestimates with Riemann Sums and Trapezoidal Approximations

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Error Bound Formulas for midpoint and trapezoid rules, sect7.7#19b

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