MATH 3 Introduction to Calculus
Naomi Tanabe
Dartmouth College
Winter 2016
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Question: How do we find the area S?
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Question: How do we find the area S?
1. Divide the interval to several strips.
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Question: How do we find the area S?
1. Divide the interval to several strips.
2. Estimate the area of each strip by using the rectangle shape.
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CAUTION!! – The area found in this way is just an approximation!
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CAUTION!! – The area found in this way is just an approximation!
Example:
Underestimate
Overestimate
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CAUTION!! – The area found in this way is just an approximation!
Example:
Underestimate
Overestimate
The actual area under the curve must be between “Underestimated area” and and “Overestimated area”.
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Estimating the area:
Notice each strip is a rectangular shape = (width)・(height)
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How do we estimate the area?
Notice each strip is a rectangular shape = (width)・(height)
Area=
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How many strips should we use to estimate the area?
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How many strips should we use to estimate the area?
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How many strips should we use to estimate the area?
The more strips you have (the skinnier each rectangular shape is), the better the approximation is!
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How many strips should we use to estimate the area?
The more strips you have (the skinnier each rectangular shape is), the better the approximation is!
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Example:
1
5