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Unit 8: Applications of Antiderivatives
Max-Min Inequality Rule for Definite Integrals
Identifier: Max-Min Inequality Rule for Definite Integrals
Method: Max-Min Inequality Rule for Definite Integrals
Example 1: Max-Min Inequality for Definite Integrals
Average Value
Average Value Examples from Actual AP Exams
Identifier: Average Value
Method: Average Value
Example 1: Average Value Integral
Mean Value Theorem for Definite Integrals
Extension of Mean Value Theorem for Definite Integrals
Identifier: Mean Value Theorem for Definite Integrals
Method: Mean Value Theorem for Definite Integrals
Example 1: Mean Value Theorem for Definite Integrals
Accumulation Tool
Integral as Accumulation Tool Examples from Actual AP Exams
Identifier: Integral as Accumulation Tool
Method: Integral as Accumulation Tool
Example 1: Integral as Accumulation Tool
Physics Relationships
Integral Physics Examples From Actual AP Exams
Identifier: Physics Relationship
Method: Physics Relationships
Example 1: Physics Relationship
Displacement vs. Distance Traveled
Displacement vs. Total Distance Examples from Actual AP Exams
Identifier: Distance vs. Displacement
Method: Distance vs. Displacement
Example 1: Distance vs. Displacement
Area Between Two Curves = Region Bounded by Two Curves
Area Between Two Curves Examples from Actual AP Exams
Identifier: Area Between Two Curves
Method: Area Between Two Curves
Example 1: Area Between Two Curves (No Calculator Allowed)
Example 2: Area Between Two Curves (Calculator Allowed)
Example 3: In Terms of y (No Calculator Allowed)
Volumes of Solids
Using Cross Sectional Areas
Cross Sectional Area Examples from Actual AP Exams
Identifier: Cross Sectional Areas
Method: Cross Sectional Areas
Example 1: Cross Sectional Areas
Disk Method
Disk Method Examples from Actual AP Exams
Identifier: Disk Method
Method: Disk Method
Example 1: About the x-axis
Example 2: About an axis other than the x-axis
Washer Method
Washer Method Examples from Actual AP Exams
Identifier: Washer Method
Method: Washer Method
Example 1: Washer Method About the x-axis
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Integral as Accumulation Tool Examples from Actual AP Exams

  1. Unit 8: Applications of Antiderivatives
  2. Accumulation Tool
  3. Integral as Accumulation Tool Examples from Actual AP Exams

Do you want to see where using integrals as an accumulation tool 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 B Q92
  • 2012 AP Calculus AB MCQ Part B Q81
  • 2013 AP Calculus AB MCQ Part B Q81
  • 2014 AP Calculus AB MCQ Part B Q81
  • 2015 AP Calculus AB MCQ Part B Q88
  • 2015 AP Calculus AB MCQ Part B Q89
  • 2016 AP Calculus AB MCQ Part A Q15
  • 2016 AP Calculus AB MCQ Part B Q84

FRQ’s

  • 2012 AP Calculus AB FRQ Part A Q1d
  • 2018 AP Calculus AB FRQ Part A Q1a
  • 2018 AP Calculus AB FRQ Part A Q1b
  • 2019 AP Calculus AB FRQ Part A Q1a
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