Accumulation and Definite Integrals

What learners will discover

• Interpret the area between a rate graph and the input axis as the accumulated (net) change in a quantity, with units, and distinguish net change from total change.
• Approximate accumulation with left, right, midpoint and trapezoid sums from tables and graphs, and justify whether an approximation over- or underestimates.
• Use definite integral notation, interpret signed area, and evaluate definite integrals with geometry, properties and a symbolic rule.
• Build and analyze an accumulation function A(x) = ∫~a~^x^ f(t) dt from the graph of f, including where A increases, decreases and has extreme values.
• Explain when a rule or estimate applies, stating the conditions (monotonic, concavity, sign of the integrand, form of the integrand) that justify it.

Lessons

1. From rate to amount 8 steps4 practiceabout 28 min
2. Approximating accumulation with sums 8 steps5 practiceabout 30 min
3. The definite integral and signed area 8 steps5 practiceabout 30 min
4. Accumulation functions 7 steps3 practiceabout 30 min
5. Symbolic rules and when they apply 8 steps4 practiceabout 30 min
6. Accumulation and definite integrals check 12 questions at the end