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Calculus BC · AP · Integration and Accumulation of Change

CED focus

Integrating Using Substitution

This topic is assessed on the AP Exam.

Multiple-choice tips

  • Decide if the item is net change, total area, or volume before integrating.
  • Decide indefinite vs definite integral from the stem.
  • Eliminate FTC confusions (swap limits changes sign).
  • Check whether area below the axis should count as negative net change.
  • On Riemann MC, identify left/right/midpoint and over/under estimate.

Free-response tips

  • State integrand meaning and units; show FTC or Riemann setup explicitly.
  • Show +C on indefinite integrals; omit only when definite.
  • Write FTC setup with limits and antiderivative evaluation.
  • Explain accumulation with units in applied FRQs.
  • Show Riemann sum notation when approximation is required.

Common traps

  • Wrong limits or missing π in volume setups
  • Dropping +C on indefinite integrals
  • Reversing limits without negating the integral
  • Treating area as always positive without reading the question

Quick checklist

  • [ ] Can write a definite integral for net change
  • [ ] Can apply FTC Part 1 or 2 correctly
  • [ ] Can interpret an integral in context with units

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