Area Under the Curve

The area between the curve and the x axis.

Accumulation of Change

The area “under” the curve—net change of a rate of change function—(under: between the curve and the x axis.)

When looking at one rate-of-change function, the accumulated change over an interval and the definite integral are equivalent, their values could be positive, negative or zero.

Net accumulation of change—the overall accumulation of change.

• Example: You are on a road trip and have your car on cruise control for 4 hours. You travel at 60 miles per hour. How far have you traveled?

Riemann Sum

Definite Integral Form