Using Accumulation Functions and Definite Integrals in Applied Contexts
Samuel Baker
5 min read
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.
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Question 1 of 10
A car's velocity is represented by the graph below. 🚗 Which shaded area represents the total distance traveled by the car from t=a to t=b?
The area above the x-axis and below the curve from a to b
The area below the x-axis and above the curve from a to b
The slope of the curve from a to b
The y-value at t=b