Integration =

1
Integration

to put together
2
Integration

• To Put Together or
• To find the sum of the parts
• To add, we use Sigma Notation S
• GOAL Find the area
• under a curve

3
Estimate the area under the curve with an UPPER
SUM and a LOWER SUM using the areas of
rectangles of width 1.
4
Estimate the area under the curve with an UPPER
SUM and a lower sum using the areas of
rectangles of width 1.
5
Summation / Sigma Notation
Expand and Calculate
Substitute 1 for i. Then substitute 2 for i.
Then substitute 3 for i, Finally
substitute 4 for i. Then ADD THE TERMS together.
6
Integration
Write using Sigma Notation
7
Integration
Write using Sigma Notation
8
4 Formulas page 254

• 1)
• 2)

• 3)
• 4)

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Constant

• Summation
• Formulas

10

• Summation
• Formulas

11

• Summation
• Formulas

12

• Summation
• Formulas

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Approximating Area
Approximate the area under
down to the x-axis from x 0 to x
2 using 4 rectangles. Give both a lower sum with
inscribed rectangles and an upper sum using
circumscribed rectangles. Suggested format
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Limit of a Summation Function

• Find the limit of s(n) as n ? 8.

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Limit of a Summation Function

• Use a formula for the sum. Then evaluate the
  limit.

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EXACT AREA
Book
Mr. Case
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Exact Area w/Limits
Find the EXACT area under
down to the x-axis from x 0 to x 2.
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Remember Antiderivatives ?Sigma Notation, Area
under a Curve and Antiderivatives are all
involved in Definite Integrals