Lesson Plan #6
Lesson Plan #53
Class: Intuitive Calculus Date: Wednesday March 3rd, 2010
Topic: The Definite Integral and Area
Aim: How do we use the Definite Integral to Find the area between a curve, the [pic]-axis, [pic], and [pic]?
Objectives:
1) Students will be able to use definite integral to find the area between a curve, the x-axis, [pic], and [pic]
Note:
HW# 53:
Page 286 #’s 15, 16, 17, 18, 2 (Break it up into 2 sections)
Do Now:
Evaluate
1) [pic]
2) [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
Assignment #1:
Set up a definite integral that yields the area of the given region.
1)
2)
3)
Assignment #2:
Sketch the region whose area is given by the definite integral.
A) [pic]
B) [pic]
C) [pic]
D) [pic]
Recall these properties of definite integrals:
Properties of Definite Integrals:
1) If [pic]is defined at [pic], then [pic]
2) If [pic]is integrable on [pic]then, [pic]
3) If [pic]is a constant, then [pic]
4) [pic]If [pic]then [pic]
5) [pic]
Assignment #3:
Use the above properties to answer the following questions
Given [pic] and [pic], find
A) [pic]
B) [pic]
C) [pic]
D) [pic]
Assignment #4:
Evaluate the definite integral
A) [pic]
B) [pic]
C) [pic]
D) [pic]
E) [pic]
F) [pic]
G) [pic]
-----------------------
[pic]
Theorem: All continuous functions are integrable. That is, if a function [pic]is continuous on an interval [pic], then its definite integral over [pic]exists.
Definition:
If [pic]is non-negative (meaning at or above the x-axis) and integrable over a closed interval [pic], then of the region bounded by [pic] , the x-axis, and the vertical lines [pic] and [pic] is given by [pic]
[pic]
[pic]
[pic]
[pic][pic] [pic]
................
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