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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)
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
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)
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Examples From Actual AP Exams

  1. Unit 6: Antiderivatives
  2. n x
  3. Examples From Actual AP Exams

Do you want to see where nx\frac{n}{x} integral problems appear on previous AP Calc exams and a video solution for those problems?
I have compiled a comprehensive list here so you don’t have to go looking all over the internet.

MCQ’s

  • 2008 AP Calculus AB MCQ Part A Q15
  • 2013 AP Calculus AB MCQ Part A Q6
  • 2013 AP Calculus AB MCQ Part A Q90
  • 2014 AP Calculus AB MCQ Part A Q4
  • 2016 AP Calculus AB MCQ Part A Q17
  • 2016 AP Calculus AB MCQ Part A Q23

FRQ’s

  • 2012 AP Calculus AB FRQ Part B Q5c
  • 2019 AP Calculus AB FRQ Part B Q5b
  • 2021 AP Calculus AB FRQ Part B Q6c
  • 2023 AP Calculus AB FRQ Part B Q3d
  • 2024 AP Calculus AB FRQ Part B Q3c
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