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Course: Integral Calculus?>?Unit 1
Lesson 2: Approximation with Riemann sums- Riemann approximation introduction
- Over- and under-estimation of Riemann sums
- Left & right Riemann sums
- Worked example: finding a Riemann sum using a table
- Left & right Riemann sums
- Worked example: over- and under-estimation of Riemann sums
- Over- and under-estimation of Riemann sums
- Midpoint sums
- Trapezoidal sums
- Understanding the trapezoidal rule
- Midpoint & trapezoidal sums
- Riemann sums review
- Motion problem with Riemann sum approximation
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Over- and under-estimation of Riemann sums
Problem
Function is continuous and decreasing.
We're interested in the area under the curve between and , and we're considering using left and right Riemann sums to approximate it.
Order the areas from least (on top) to greatest (on bottom).