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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

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)

Previous Lesson

Identifier: Inverse Trig Antiderivatives

Unit 6: Antiderivatives
Six Inverse Trig Functions
Identifier: Inverse Trig Antiderivatives

Your equation includes one of the six inverse trig function special cases.

Previous Lesson

Taking AP Calc next year? Work with me this summer & get the head start you need.

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