## Introduction to Integration

Read this section to learn about area. Work through practice problems 1-9.

### Some Applications of "Area"

#### Total Accumulation as "Area"

In the previous examples, the function represented a **rate** of travel (miles per hour), and the area represented the **total** distance traveled. For functions representing other **rates **such as the production
of a factory (bicycles per day), or the flow of water in a river (gallons per minute) or traffic over a bridge (cars per minute), or the spread of a disease (newly sick people per week), the area will still represent the **total** amount
of something.

##### "Area" as a Total Accumulation

If represents a positive rate (in units per time interval) at time , then the "area" between the graph of f and the t–axis and the vertical lines at times and will be the total units which accumulate between times and . (Fig. 17)

For example, Fig. 18 shows the flow rate (cubic feet per second) of water in the Skykomish river at the town of Goldbar in Washington state. The area of the shaded region represents the total volume (cubic feet) of water flowing past the town during the month of October:

Total water = "area"

= area of rectangle + area of the triangle

(For comparison, the flow over Niagara Falls is about ).

**Practice 9: **Fig. 19 shows the number of telephone calls made per hour on a Tuesday. Approximately how many calls were made between 9 pm and 11 pm?