The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Accumulation and mixed calculus review
Recover amounts from rates and initial values.
Distinguish net change, final amount and total variation.
Evaluate variable-limit integrals and check all extrema on a closed interval.
An integral of a rate gives a change: add the initial amount. Find sign changes before calculating total distance or total variation. A variable upper limit can be handled by evaluating the integral explicitly, then differentiating the result.