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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U-Substitution

Unit 6: Antiderivatives U-Substitution

U-substitution is how you take the antiderivative (undo the derivative) of an equation that came from a Chain Rule  derivative. U-substitution is an antiderivative process that takes an integral that you don’t know how to solve, and rewrites the integral so that it becomes an integral you do know how to solve (i.e., turns it into either a power rule or a special case  antiderivative).

My u-substitution method is different than many teachers that I have seen. Believe me my method works, my method is easier, my method works better than the more standardized way of teaching u-substitution, and my method is completely accepted by those who grade the AP Calculus Exam because it is mathematically the same. My method does not require you to find what you need to multiply by or “see” what you need to multiply by in order to substitute in your u . My method requires no “seeing” anything, and just works.

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