Antiderivatives From Derivatives of Basic Functions

 

Antidifferentiation

Antiderivatives and indefinite integrals are defined. Constants of integration and integrands are also defined.

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Antidifferentiation: Guess-and-Check

Guess-and-check method for finding antiderivatives. Includes an example and some helpful rules.

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Introduction to Anti-Derivatives

Definition of the indefinite integral or anti-derivative and its use in finding information about a function when its derivative is known.

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Non-Uniqueness of Anti-Derivatives

Discussion of the fact that any constant can be added to an antiderivative without changing the validity of that antiderivative.

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Anti-Derivatives by Inspection

Applying differentiation rules backwards to find anti-derivatives. A list of types of functions that can or cannot be anti-differentiated. Linearity of the operation of anti-differentiation.

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Basic Techniques for Integrals

Rules for integrating polynomials and other simple integrals by inspection, as well as techniques for integrating by substitution, parts, and partial fractions.

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Evaluating Definite Integrals

Five-part problem evaluating integrals involving the substitution method, logarithmic functions, and trigonometric functions.

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Antiderivatives Using Polynomial Division

Computing the antiderivative of a fraction of two polynomials.

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Indefinite Integrals

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Three integrals to be evaluated.

Two integrals to be evaluated.

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Trigonometric and Logarithmic Integrals

Deriving a trigonometric formula and differentiating a logarithmic expression, then using those results to evaluate two integrals.

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Definite Integrals

Two integrals to be evaluated.

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Trigonometric Formulas and Identities

A list of trigonometric and inverse trigonometric identities and formulas involving integrals and derivatives.

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Differentiation Formulas: Polynomials, Products, Quotients

Five questions which involve taking derivatives and antiderivatives of polynomials, finding the points on a graph which have horizontal tangent lines, and finding derivatives of rational functions.

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Differentials and Indefinite Integration

Three questions which involve evaluating five differentials and twenty indefinite integrals using a range of techniques.

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Inverse Trigonometric and Hyperbolic Functions

Six questions which involve evaluating integrals and derivatives of these functions, as well as graphing them and finding tangent lines or average values.

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