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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