Identifier: Integral as Accumulation Tool

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, $\frac{\mathit{words}}{\mathit{minute}}=\frac{\mathit{dw}}{\mathit{dt}}$, 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 .