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Calculus Series - Concepts and Formulas
Integration Fundamentals and Basic Formulas (CLS-CF4)

This sheet provides a comprehensive review of all of the most important topics, concepts and formulas covering integration fundamentals and basic integration formulas. Each concept is explained in detail, with detailed illustrations. Unlike charts and notes, this Concepts and Formulas sheet answers questions about how to use the concepts - how to actually solve problems with them, it doesn't just list facts and formulas. There is even an example, or two, for each concept, to help you to nail down the central ideas.

Topics Covered:

• Constructing the definite integral
• Partitions of closed intervals
• Riemann sums
• The definite integral of a function over an interval
• The area of the region between the graph of a function and the x-axis on a closed interval
• The parts of a definite integral
• The integrand and its properties
• The limits of integration
• Integrable functions
• Fundamental properties of Sigma notation and some special sums
• Fundamental properties of definite integrals
• Definite integral comparison properties
• Antiderivatives
• The Fundamental Theorem of Calculus
• Integration as the inverse of differentiation
• Evaluating integrals: basic power rule
• The general power rule
• Integration by substitution
• Change of variables
• The area between two curves
• Basic integration formulas
• Basic trigonometric and hyperbolic integrals
• Some special integrals

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