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Accumulation, Average Value, and Net Change worksheets

Interpret definite integrals as signed change, average value, and recovery from an initial amount.

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Interpret definite integrals as signed change, average value, and recovery from an initial amount.

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Method, assumptions, and units stay visible

Each generated problem includes bounded solvable givens. Worked pages show the theorem, formula, substitution, or physical slice used to reach the result.

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Connect rate integrals to contextual quantities and units.

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The governing formula, substituted givens, and a labeled conclusion.

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  • Keep units or domains beside each line.
  • Ask students to name the theorem or formula before substituting.
  • Distinguish exact values from labeled approximations.

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Math SheetNameScoreTeacherDateAccumulation, Average Value, and Net ChangeUse a definite integral to interpret signed change, average value, or recovery from an initial value. Label estimated table results.1.table t: 0, 2; r(t): 4, 12, for 0<=t<=2, with t in seconds and r(t) in meters per seconds. Use a trapezoid estimate. Find signed net change.2.r(t)=2t-1, for 0<=t<=2, with t in seconds and r(t) in meters per seconds. Find the average value of the rate.State assumptions, domains, units, and approximation methods.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateAccumulation, Average Value, and Net ChangeUse a definite integral to interpret signed change, average value, or recovery from an initial value. Label estimated table results.3.r(t)=3t-3, for 0<=t<=4, with t in seconds and r(t) in meters per seconds. Find signed net change.4.r(t)=2t+3, for 0<=t<=3, with t in seconds and r(t) in meters per seconds. If Q(0)=11 meters, find Q(3).State assumptions, domains, units, and approximation methods.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateAccumulation, Average Value, and Net ChangeUse a definite integral to interpret signed change, average value, or recovery from an initial value. Label estimated table results.5.table t: 0, 2; r(t): 2, 6, for 0<=t<=2, with t in seconds and r(t) in meters per seconds. Use a trapezoid estimate. If Q(0)=17 meters, find Q(2).6.table t: 0, 3; r(t): -2, 10, for 0<=t<=3, with t in seconds and r(t) in meters per seconds. Use a trapezoid estimate. Find the average value of therate.State assumptions, domains, units, and approximation methods.math-sheet.comPage 3 of 3

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