These will usually be word problems where you are given the rate that something is occurring, *
usually with respect to
**
time
*. You are then asked for the *
net
*or *
total
*amount of the *
units
* “on the top” (numerator) of your rate of change.

You are given a rate of change of words *
per
*minute, $\frac{\textcolor[rgb]{}{\mathit{words}}}{\textcolor[rgb]{}{\mathit{minute}}}=\frac{\textcolor[rgb]{}{\mathit{dw}}}{\textcolor[rgb]{}{\mathit{dt}}}$, and you are asked, “How many *
total
*words you could learn in 10-minutes?” Or you are given a rate of change in gallons *
per
*minute and asked about the total gallons over a period of time.

Remember that a word like *
per
* is helping you to identify rates of change which are your derivatives.It is that derivative you can take the definite integral of to get the *
accumulate
**
amount
*.

You will also see this application applied frequently with a *
table of values
* where the *
y-values
*of the table are a *
rate of change
*(Ex: a table with *
velocity
*at certain times). In these situations, you will need to use *
Riemann Sums
*to get your estimation for the total *
accumulation
*.

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