Lesson Plan #6



Lesson Plan #67

Class: AP Calculus Date: Tuesday March 5th, 2012

Topic: Using the integration rules for exponential functions.

Aim: How do we use the integration rules for Exponential functions?

Objectives:

1) Students will be able to use the integration rules for exponential functions

HW# 67:

Page 312 #’s 9, 10, 11, 12, 13

Do Now:

1) Evaluate [pic] (Hint: Let [pic])

2) Find the average value of [pic]over the interval [pic]

3) Find the derivative of [pic]

4) Find the antiderivative of [pic]

5) What is the formula for [pic]?

Procedure:

Write the Aim and Do Now

Get students working!

Take attendance

Give back work

Go over the HW

Collect HW

Go over the Do Now

Theorem: Integration Rules for Exponential Functions

Example: Evaluate

1) [pic]

2) [pic]

3) [pic]

4) [pic]

5) [pic]

Example:

Find the area of the shaded region bounded by [pic]

On Your Own:

Evaluate

1) [pic]

2) [pic]

3) [pic]

4) [pic]

5) [pic]

6) [pic]

7) Find the area of the region bounded by the graphs of the equations.

[pic]

If Enough time: Do these sample Calculus AP AB questions to test your understanding of this topic.

Find each indefinite integral

1) [pic]

2) [pic]

3) [pic]

4) [pic] (Hint: Divide)

Evaluate

5) [pic]

6) [pic]

7) [pic]

8) [pic]

9) [pic]

10) [pic]

Free Response Questions: Calculator Question (Skylight 273)

1) Methane is produced in a cave at a rate of [pic]liters per hour at time [pic]hours. The initial amount of methane in the cave at time [pic]is 20 liters. At time [pic]hours, a pump begins to remove the methane gas at a constant rate of 1.5 liters per hours

A) At what time [pic]during the interval [pic]hours is the amount of methane increasing most rapidly?

B) What is the total amount of methane in the cave at time [pic]?

C) What is the average rate of methane accumulation in the cave over the time interval [pic]?

-----------------------

Draw the graph

1. [pic] 2. [pic]

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