Unit 6: Antiderivatives

Antiderivatives Overview
Definite Integrals = Fundamental Theorem of Calculus Part 2
3 Topics
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
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
Identifier: Antiderivative of Constants
Method: Antiderivative of Constants
Example 1: Antiderivative of a Constant
Rule 2: Power Rule
6 Topics
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
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
Identifier: Inverse Trig Antiderivatives
Method: Inverse Trig Antiderivatives
Example 1: Definite Integral Inverse Trig
Example 1: Indefinite Integral Inverse Trig
e ( nx )
4 Topics
Identifier: e^(x) Antiderivative
Method: e^(x) Antiderivatives
Example 1: e^(x) Definite Integral
Example 1: e^(ax) Indefinite Integral
a ( nx )
4 Topics
Identifier: a^(nx) Antiderivative
Method: a^(nx) Antiderivative
Example 1: Definite Integral Exponential Function
Example 1: Indefinite Integral of Exponential Function
n x
4 Topics
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
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
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
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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The Two Main Antiderivative Rules

Unit 6: Antiderivatives The Two Main Antiderivative Rules

Just like you had specific rules for finding the derivative (i.e., power rule, product rule, etc.), you will have specific rules for finding the antiderivative. The good news is that there are far fewer antiderivative rules that you need to know. The antiderivative rules are the same regardless of whether you are finding a definite integral or an indefinite integral. For each rule I will provide an example that shows how it works with a definite integral or an indefinite integral.

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