Calculus
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Find exact indefinite integrals of polynomial, reciprocal integer-power, and reciprocal rational-power functions while preserving the original real domain.
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Riemann Sum Tables worksheets
Calculate exact left-endpoint, right-endpoint and midpoint Riemann-sum area estimates from complete tables on uniform intervals.
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Find the rectangle width, select the correct table values and multiply their sum by the width.
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Customize this worksheetTurn a table into equal-width rectangles
Each task displays every endpoint and midpoint needed for its interval. Find the common width, choose the samples named by the method, then multiply the height sum by the width.
Learning objective
What this activity builds
Use tabulated function values to compute exact Riemann-sum area estimates.
Worked example
Which values are used for a midpoint sum?
Use the table values halfway through each subinterval.
For n equal rectangles, select the n midpoint samples, add their heights and multiply by the common width.
Teaching notes
Make the practice count
- Compute the common width before selecting table values.
- Mark the selected x-values directly in the table.
- Keep the width outside the height sum until the final multiplication.
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Choose 4 or 8 tasks, one or more sampling methods, and 3, 4 or 5 rectangles. Every task includes its own complete table.
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