AP Calculus AB / Unit 6: Integration and Accumulation of Change
6.1 Exploring Accumulations of Change
Notes
If you know a rate, the area under the rate graph gives the total change.
- Rate × time = amount, when the rate is constant.
- Area above the axis adds; area below the axis subtracts.
Practice
Water flows in at a constant 3 gallons per minute for 10 minutes. The total added is:
Rate times time.
The area under a velocity graph from $t=0$ to $t=5$ represents:
Accumulating velocity gives change in position.
Area below the $t$-axis on a rate graph represents:
Negative rate means the amount goes down.
Ready for more? Take the Unit 6 test.