Calculus I · Unit 3A · review
Unit 3A Review: Integral Foundations and Techniques
Learn Unit 3A Review: Integral Foundations and Techniques through clear explanation, worked examples, visual reasoning, checks, and connected integral-calculus practice.
Section overview
Review, practice, exams, and answer keysWhat this section is building
Learn Unit 3A Review: Integral Foundations and Techniques through clear explanation, worked examples, visual reasoning, checks, and connected integral-calculus practice.
A complete response carries setup, method, computation, bounds or constants, units, interpretation, and an independent verification.
Attempt the entire problem first, then use one answer at a time to locate the earliest reasoning decision that needs repair.
Reading a key before modeling the problem or treating every mismatch as algebra when the first error was conceptual.
Unit 3A Review
Core ideas
• Antiderivatives reverse differentiation and form families differing by constants. • Riemann sums approximate continuously distributed totals. • Definite integrals are signed accumulations and limits of Riemann sums. • The Fundamental Theorem links differentiation and integration. • Substitution reverses the chain rule; integration by parts reverses the product rule. • Numerical methods estimate integrals when exact antiderivatives are unavailable. • Improper integrals are defined by limits and may converge or diverge.
Find .
Approximate using four midpoint rectangles.
Differentiate .
Evaluate .
Evaluate .
Evaluate by partial fractions.
Determine convergence of .
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