Area & Definite Integral Applications

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Presentation transcript:

Area & Definite Integral Applications Lesson 7.3B

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

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

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

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 ?

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 ?

Assignment Lesson 7.3B Page 389 Exercises 23-33 All