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Unit 6: Antiderivatives

Antiderivatives Overview

Definite Integrals = Fundamental Theorem of Calculus Part 2

Definite Integral Examples From Actual AP Exams

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.

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

Identifier: Antiderivative of Constants

Method: Antiderivative of Constants

Example 1: Antiderivative of a Constant

Rule 2: Power Rule

Power Rule Integral Examples From Actual AP Exams

Identifier: Power Rule Antiderivative

Method: Power Rule Antiderivative

Example 1: Definite Integral Power Rule

Example 1: Definite Integral Power Rule (Video)

Example 1: Indefinite Integral Power Rule

Example 1: Indefinite Integral Power Rule (Video)

Example 2: Definite Integral Power Rule

Example 2: Definite Integral Power Rule (Video)

Example 2: Indefinite Integral Power Rule

Example 2: Indefinite Integral Power Rule (Video)

Special Case Antiderivatives (The ones you have to memorize)

Special Case Antiderivatives

Six Trig Functions

Trig Function Integral Examples From Actual AP Exams

Identifier: Trig Function Antiderivatives

Method: Trig Function Antiderivatives

Example 1: Definite Integral Trig Function

Example 1: Definite Integral Trig Function (Video)

Example 2: Indefinite Integral Trig Functions

Example 2: Indefinite Integral Trig Functions (Video)

Six Inverse Trig Functions

Identifier: Inverse Trig Antiderivatives

Method: Inverse Trig Antiderivatives

Example 1: Definite Integral Inverse Trig

Example 1: Definite Integral Inverse Trig (Video)

Example 2: Indefinite Integral Inverse Trig

Example 2: Indefinite Integral Inverse Trig (Video)

e^{(nx)}

Determine the Integral of ‘e’ Examples from Actual AP Exams

Identifier: e^(x) Antiderivative

Method: e^(x) Antiderivatives

Example 1: e^(x) Definite Integral

Example 1: e^(x) Definite Integral (Video)

Example 2: e^(ax) Indefinite Integral

Example 2: e^(ax) Indefinite Integral (Video)

a^{(nx)}

Identifier: a^(nx) Antiderivative

Method: a^(nx) Antiderivative

Example 1: Definite Integral Exponential Function

Example 1: Definite Integral Exponential Function (Video)

Example 2: Indefinite Integral of Exponential Function

Example 2: Indefinite Integral of Exponential Function (Video)

\frac{n}{x}

Examples From Actual AP Exams

Identifier: ln(x) Antiderivative

Method: ln(x) Antiderivative

Example 1: Definite Integral ln(x)

Example 1: Definite Integral ln(x) (Video)

Example 2: Indefinite Integral ln(x)

Example 2: Indefinite Integral ln(x) (Video)

U-Substitution

U-Substitution Examples From Actual AP Exams

Identifier: U-Substitution

Method: U-Substitution

Example 1: Indefinite Integral U-Substitution

Example 1: Indefinite Integral U-Substitution (Video)

Example 2: Definite Integral U-Substitution

Example 2: Definite Integral U-Substitution (Video)

Initial Value Problems: Finding the +C

Initial Value Problems

Initial Value Integral Problem Examples From Actual AP Exams

Identifier: Initial Value Problem

Method: Initial Value Problem

Example 1: Initial Value Problem

Example 1: Initial Value Problem (Video)

Fundamental Theorem of Calculus Part 1

Fundamental Theorem of Calculus Part 1

Fundamental Theorem of Calculus Part 1 Examples from Actual AP Exams

Identifier: Fundamental Theorem of Calculus Pt. 1

Method: Fundamental Theorem of Calculus Pt. 1

Example 1: Fundamental Theorem of Calculus Pt. 1

Example 1: Fundamental Theorem of Calculus Pt. 1 (Video)

Example 2: Fundamental Theorem of Calculus Pt. 1

Example 2: Fundamental Theorem of Calculus Pt. 1 (Video)

Identifier: ln(x) Antiderivative

Unit 6: Antiderivatives
n x
Identifier: ln(x) Antiderivative

Your equation includes the base case $\frac{n}{x^{1}}$ .

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