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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