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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: 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
Trig Function Integral Examples From Actual AP Exams
Identifier: Trig Function Antiderivatives
Method: Trig Function Antiderivatives
Example 1: Definite Integral Trig Function
Example 1: Indefinite Integral Trig Functions
Six Inverse Trig Functions
Identifier: Inverse Trig Antiderivatives
Method: Inverse Trig Antiderivatives
Example 1: Definite Integral Inverse Trig
Example 1: Indefinite Integral Inverse Trig
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^(ax) Indefinite Integral
a ( nx )
Identifier: a^(nx) Antiderivative
Method: a^(nx) Antiderivative
Example 1: Definite Integral Exponential Function
Example 1: Indefinite Integral of Exponential Function
n x
Examples From Actual AP Exams
Identifier: ln(x) Antiderivative
Method: ln(x) Antiderivative
Example 1: Definite Integral ln(x)
Example 1: Indefinite Integral ln(x)
U-Substitution
U-Substitution
U-Substitution Examples From Actual AP Exams
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
Initial Value Integral Problem Examples From Actual AP Exams
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
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 2: Fundamental Theorem of Calculus Pt. 1
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Fundamental Theorem of Calculus Part 1 Examples from Actual AP Exams

  1. Unit 6: Antiderivatives
  2. Fundamental Theorem of Calculus Part 1
  3. Fundamental Theorem of Calculus Part 1 Examples from Actual AP Exams

Do you want to see where Fundamental Theorem of Calculus Part 1 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 Q17
  • 2012 AP Calculus AB MCQ Part A Q15
  • 2012 AP Calculus AB MCQ Part A Q17
  • 2012 AP Calculus AB MCQ Part A Q26
  • 2013 AP Calculus AB MCQ Part A Q11
  • 2013 AP Calculus AB MCQ Part A Q20
  • 2014 AP Calculus AB MCQ Part A Q26
  • 2014 AP Calculus AB MCQ Part B Q88
  • 2015 AP Calculus AB MCQ Part A Q17
  • 2015 AP Calculus AB MCQ Part B Q83
  • 2016 AP Calculus AB MCQ Part A Q14
  • 2016 AP Calculus AB MCQ Part A Q20

FRQ’s

  • 2012 AP Calculus AB FRQ Part B Q3b
  • 2018 AP Calculus AB FRQ Part A Q1d
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