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Calculus Series - Concepts and Formulas
Integration Techniques 2, Integration Applications 1 (CLS-CF6)

This sheet provides a comprehensive review of all of the most important topics, concepts and formula covering integration techniques and applications of integration. 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:

  • Approximate integration
  • The Trapezoidal Rule
  • The nth Trapezoidal rule error
  • Simpson's rule
  • The nth Simpson's rule error
  • Improper integrals
  • Volumes of solid regions by cross-sections
  • Volumes of solids of revolution by the disc
  • The washer and shell methods
  • Work
  • Hooke's Law
  • The restoring force
  • The spring constant

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Algebra Series:
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Graphing Fundamentals 1 - Relations and Functions, Function Tests (ALG-CF9)
Graphical Functions 2 - Symmetries, Intercepts, Zeros and Slopes (ALG-CF10)
Graphical Fundamentals 3 - Maxima and Minima, Lines and Translations (ALG-CF11)
Solutions of Systems of Linear Equations and Inequalities in Two Variables 1 (ALG-CF12)
Solutions of Systems of Linear Equations and Inequalities in Two and Three Variables (ALG-CF13)
Solutions of Systems of Linear Equations in Three Variables (ALG-CF14)
Partial Fraction Decompositions (ALG-CF15)
Matrix Fundamentals, Basic Operations on Matrices (ALG-CF16)
Types of Matrices, Matrix Solutions of Systems of Linear Equations (ALG-CF17)
Inverse Matrices, Matrix Equations, Fundamentals of Determinants (ALG-CF18)
Determinant Solutions of Linear Systems, Applications of Determinants (ALG-CF19)
Quadratic Functions, Techniques for Solutions of Quadratic Equations (ALG-CF22)
Polynomial Functions and Equations (ALG-CF24)
Real Solutions of Polynomial Equations (ALG-CF25)
Approximations of Real Polynomial Functions, Rational Functions 1 (ALG-CF26)
Rational Functions 3 and Variations (ALG-CF28)
Inverse and Radical Functions, Exponential Functions 1 (ALG-CF29)
Exponential Functions 2, Logarithmic Functions (ALG-CF30)
Sequences and Series 1 (ALG-CF32)
The Binomial Theorem, Mathematical Induction (ALG-CF33)
Trigonometry Series:
Trigonometric Functions and Applications (TRG-CF2)
Periodicity and Trigonometric Graphs (TRG-CF3)
Inverse Trigonometric Functions, Verifying Identities (TRG-CF4)
Trigonometric Identities 1 (TRG-CF5)
Trigonometric Identities 2, Trigonometric Equations (TRG-CF6)
Calculus Series:
Limits and Differentiation Formulas (CLS-CF1)
Applications of Differentiation 1 (CLS-CF2)
Applications of Differentiation 2 (CLS-CF3)
Integration Fundamentals and Basic Formulas (CLS-CF4)
Integration Techniques 1 (CLS-CF5)
E-Books
Table of Derivatives and Integrals with Selected Special Functions (CLS-EB-R3)

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Last Update: 08/25/14