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In this section, we will introduce the definite integral and begin looking at what it represents and how to calculate its value.
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What is the “signed” area bounded by the graph of a function y = f(x), the x-axis, x = a and x = b?
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Why “signed” area? How do we calculate it? What does it represent?
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Let f be a function defined at all but finitely many points of [a, b]. The definite integral of f from a to b, denoted, is the “signed” area of the region bounded by the graph of y = f(x), the x-axis, x = a and x = b.
![Let f be a function defined at all but finitely many points of [a, b].](http://images.slideplayer.com./25/8093663/slides/slide_4.jpg "The definite integral of f from a to b, denoted, is the signed area of the region bounded by the graph of y = f(x), the x-axis, x = a and x = b..")
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Consider the graph of y = f(x) below. Find: (a) (b) (c) (d)
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Find by using the definition.
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The following integral statements are true: 1. 2. 3. If a < c < b, then 4. 5.
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Suppose Find:
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