Unit 6: Antiderivatives

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Antiderivatives Overview

Definite Integrals = Fundamental Theorem of Calculus Part 2 3 Topics

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Riemann Sums Become Definite Integrals

The Actual Fundamental Theorem of Calculus Part 2

Net Area vs Total Area

Indefinite Integrals

The Two Main Antiderivative Rules

The Two Main Antiderivative Rules

Always Step 1: Simplify and Look for Algebraic Rewrites. 5 Topics

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Roots or Radicals

x’s On the Bottom of a Fraction

Trig Functions Raised to a Power

Look to Make Your Life Easier

Check the Bounds (NEW)

Rule 1: Constants 3 Topics

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Identifier: Antiderivative of Constants

Method: Antiderivative of Constants

Example 1: Antiderivative of a Constant

Rule 2: Power Rule 6 Topics

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Identifier: Power Rule Antiderivative

Method: Power Rule Antiderivative

Example 1: Definite Integral Power Rule

Example 1: Indefinite Integral Power Rule

Example 2: Definite Integral Power Rule

Example 2: Indefinite Integral Power Rule

Special Case Antiderivatives (The ones you have to memorize)

Special Case Antiderivatives

Six Trig Functions 4 Topics

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Identifier: Trig Function Antiderivatives

Method: Trig Function Antiderivatives

Example 1: Definite Integral Trig Function

Example 1: Indefinite Integral Trig Functions

Six Inverse Trig Functions 4 Topics

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Identifier: Inverse Trig Antiderivatives

Method: Inverse Trig Antiderivatives

Example 1: Definite Integral Inverse Trig

Example 1: Indefinite Integral Inverse Trig

e ( nx ) 4 Topics

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Identifier: e^(x) Antiderivative

Method: e^(x) Antiderivatives

Example 1: e^(x) Definite Integral

Example 1: e^(ax) Indefinite Integral

a ( nx ) 4 Topics

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Identifier: a^(nx) Antiderivative

Method: a^(nx) Antiderivative

Example 1: Definite Integral Exponential Function

Example 1: Indefinite Integral of Exponential Function

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Identifier: ln(x) Antiderivative

Method: ln(x) Antiderivative

Example 1: Definite Integral ln(x)

Example 1: Indefinite Integral ln(x)

U-Substitution

U-Substitution 4 Topics

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Identifier: U-Substitution

Method: U-Substitution

Example 1: Indefinite Integral U-Substitution

Example 2: Definite Integral U-Substitution

Initial Value Problems: Finding the +C

Initial Value Problems 3 Topics

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Identifier: Initial Value Problem

Method: Initial Value Problem

Example 1: Initial Value Problem

Fundamental Theorem of Calculus Part 1

Fundamental Theorem of Calculus Part 1 4 Topics

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Identifier: Fundamental Theorem of Calculus Pt. 1

Method: Fundamental Theorem of Calculus Pt. 1

Example 1: Fundamental Theorem of Calculus Pt. 1

Example 2: Fundamental Theorem of Calculus Pt. 1

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