Antiderivatives and integration tools
What students will learn
Select and verify basic and BC integration methods, including parts, linear partial fractions, and separately defined improper limits.
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: Integrating Using Integration by Parts →
Reverse the product rule with a justified parts choice, compatible bounds, and a derivative check.
Read: Integrating Using Linear Partial Fractions →
Decompose distinct nonrepeating linear factors, verify the algebra, and preserve excluded inputs.
Read: Evaluating Improper Integrals →
Define improper integrals using separate finite one-sided limits, rather than cancellation across a pole.
Read: Selecting Techniques for Antidifferentiation →
Combine the shared AB method-selection lesson with its genuine BC addition: parts, distinct linear partial fractions, and interval limits.
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.
Select a method and justify improper convergence →
Decompose the integrand on finite intervals, then take an endpoint limit to establish a finite value.
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.