Antiderivatives and integration tools
What students will learn
Select and verify integration methods, preserving variables, bounds, and domain restrictions.
Before this topic
- Accumulation and the Fundamental Theorem
- Derivative rules and algebraic identities
Read and connect
Read: Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation →
Reverse familiar derivative rules to find antiderivative families on their valid intervals.
Read: Integrating Using Substitution →
Match an inside expression and its differential, changing both bounds or returning to the original variable.
Read: Integrating Functions Using Long Division and Completing the Square →
Use long division or completing the square to expose a basic integral without changing its domain.
Read: Selecting Techniques for Antidifferentiation →
Select an integration method from the integrand and inspect the interval before exact or numerical evaluation.
Check understanding
Use the complete prompt to make student reasoning visible, then consult the separate worked reasoning and criteria. A reading completion tick records reading history.
Check the interval and integrate after division →
Verify the denominator on the bounds, use long division, and evaluate the endpoint difference.
Choose a method for a rational integral →
Use long division to expose basic antiderivatives and retain the excluded input.
Standards and earlier reading lists
These topic placements organize reading. Edition-qualified Standards mappings and the existing complete unit task sets retain their reviewed scope.