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2 min read•june 8, 2020

Anusha Tekumulla

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

**Accumulation problems** are word problems where the **rate of change of a quantity is given** and **we are asked to calculate the value of the quantity accumulated over time**. These problems are solved using definite integrals.

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

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**.

In order to understand this concept, let’s look at an example from an actual AP exam.

**2000 AB FRQ #4**: In this question, water was being pumped into a tank at the constant rate of 8 gallons per minute and leaking out at the rate of √(t+1) gallons per minute. At time t = 0 we are told there are 30 gallons of water in the tank. 🥛

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.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 – 14/3 gallons.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

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