2 min readβ’june 8, 2020

Anusha Tekumulla

π₯**Watch: AP Calculus AB/BC - ****Interpreting the Meaning of a Derivative/Integral**

For this topic, youβll need to know how to do two things: **interpret the meaning of a definite integral** and **determine the net change of an accumulation problem.Β **

In order to interpret the meaning of a definite integral, you must know two important things. Firstly, **a function defined as an integral represents an accumulation of a rate of change**. Second, **the definite integral of the rate of change of a quantity over an interval gives the net change of that quantity over that interval**.Β

In order to understand this concept, letβs look at an example from an actual AP exam.Β

- The
**first**part of the question asked for the amount of water that leaked out of the tank in the first 3 minutes. To solve this, you must integrate the leak function from 0 to 3.Β - The
**next**part asked for the amount of water in the tank after t minutes. So we start with 30 gallons and add the amount put in which is 8 gallons per minute for 3 minutes of 24 gallons. Then we subtract the amount that leaked out from the first part. The amount is 30 + 24 β 14/3 gallons.Β - The
**third**part asked for an expression for*A(t)*, the amount of water at any*t*. So following on the second part we have either

Browse Study Guides By Unit

πUnit 1 β Limits & Continuity

π€Unit 2 β Fundamentals of Differentiation

π€π½Unit 3 β Composite, Implicit, & Inverse Functions

πUnit 4 β Contextual Applications of Differentiation

β¨Unit 5 β Analytical Applications of Differentiation

π₯Unit 6 β Integration & Accumulation of Change

πUnit 7 β Differential Equations

πΆUnit 8 β Applications of Integration

π¦Unit 9 β Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)

βΎUnit 10 β Infinite Sequences & Series (BC Only)

π§Multiple Choice Questions (MCQ)

βοΈFree Response Questions (FRQ)

πBig Reviews: Finals & Exam Prep

Β© 2023 Fiveable Inc. All rights reserved.