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Subject: Math Analysis and Trig |
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1. Topic-
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2. Content-
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What is the difference between indefinite integrals and definite
integrals?
- The main difference is that a definite integral is an exact number
because it has lower and upper limits, usually written as b and a.
What can a definite integral be used to find?
- The area under a curve from b to a. This can also be done by making
a lot of rectangles within the graph, but this is only an approximation.
In a definite integral, there is an infinitive number of boxes
Approximations
- Over summation- bigger than actual area
- Under summation- smaller than actual area
- Trapezoidal summation- divide into trapezoids 1/2 (b1-b2)h
Area as a Limit
- Infinite number of boxes
- First, find anti-derivative (integral). Then, plug in your upper
and lower limits. You will get a number answer.
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3. Goals: Aims/Outcomes-
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1. teach students what a definite integral is
2. teach students how a definite integral is different from an indefinite
integral
3. teach students what a definite integral can be used to find
4. teach students how to do definite integral problems |
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4. Materials and Aids-
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| White board, dry erase markets, pencils, paper, erasers |
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5. Procedures/Methods-
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A. Introduction-
1. draw a graph of a curve. Draw over-summation, under-summation,
and trapezoidal summations.
2. Explain area as a limit, and how it is the most accurate |
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B. Development-
1. practice finding anti-derivatives
2. practice plugging in the limits a and b into a monomial
3. teach the format if there is more than one term |
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C. Practice-
1. put sample problem on board, ask class to try to solve alone
2. If students have questions, do the problems in front of the class.
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D. Independent Practice-
Give students worksheet with problems- worksheet should have one
example so they remember how to do it
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