Definite Integrals

1
Definite Integrals

• Section 4.3

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The Definite Integral
The definite integral as the area of a region
If f is continuous and non-negative on the
closed interval a b then the area of the
region bounded by the graph of f the x-axis
and the vertical lines x a and x b is given
by   Area  This is called the definite
integral.  
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The Definite Integral

where ci is any point in the ith interval
and    
  At this point we evaluate a
definite integral using area formulas of common
geometric regions if possible. (In the next
section we will calculate the definite integral
using other methods)
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Using Common Geometric Figures
Example
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Using Common Geometric Figures
Example
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Using Common Geometric Figures
Example
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Using Common Geometric Figures
Example
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Properties of the Definite Integral
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Definite Integrals
area above area below
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Properties
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Example
If
and
then find
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Example
Set up a definite integral that yields the area
of the region.
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Example
Set up a definite integral that yields the area
of the region.
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Homework

• Section 4.3 page 278 13 19 odd 23 43 odd