1. Area & Definite Integral Applications
Lesson 7.3B

2. Interpreting Area Under the Curve
Consider a function which is telling us the rate of change of a quantity
What we call the marginal cost (or profit, etc.)
Suppose the graph shows marginal sales
m(t)
Change in Sales
Months

3. Interpreting Area Under the Curve
For a specific point in time, t = a
The change in sales is m(a)
The area of a rectangle approximates the amount of sales for a time period a
m(a) Δt
m(t)
Change in Sales
Months

4. Interpreting Area Under the Curve
The total area under the marginal sales curve will be the total sales
We use the definite integral
m(t)
Change in Sales
Total sales
Months

5. Approximating without a Formula
Use the graph to approximate the total increase in BTU's from hours 9 through 20
C(t)
What is Δt ?

6. Approximating without a Formula
Consider a table of times and velocities
Remember that velocity is rate of change of distance
Snidly Fizbane's pencil is clocked in inches per second at specified times
Approximate the total distance traveled by his pencil
t (sec) 1 2 3
v (in/sec) 10
6.5 6
5.5
What is Δt ?

7. Assignment
Lesson 7.3B
Page 389
Exercises All