Using Accumulation Functions and Definite Integrals in Applied Contexts
Samuel Baker
5 min read
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Study Guide Overview
This study guide covers accumulation problems in calculus, focusing on their application. It explains how to solve these problems by identifying the rate of change function, setting up and evaluating a definite integral, and applying any given initial conditions. Examples include calculating displacement from velocity and determining mosquito population growth using a given rate function and initial population size. A walkthrough of a 2004 AP Calculus AB free-response question illustrates the process.
#8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
Welcome to the third topic in Unit 8! In this key topic, we’ll be learning more about what an accumulation problem is and how to solve one. For a more in-depth review of how to take an integral, take a look at Unit 6!
#⛰️ Accumulation Problems
So before we learn how to solve an accumulation problem, we need to know what an accumulation problem is in the first place. The picture below is a visual representation of the graphical meaning of an integral. 📈
To calculate the integral of a function, you are essentially taking the area that is under the curve! More specifically in an accumulation problem, you are taking the integral of the rate of change function that you are given.
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A graph that represents what the integral stands for, which is the area under the curve.
Image Courtesy of Nagwa
#📝 Walkthrough of an Accumulation Problem
This will be a very simple example ...
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