 # 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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In this section, we will introduce the definite integral and begin looking at what it represents and how to calculate its value.

What is the “signed” area bounded by the graph of a function y = f(x), the x-axis, x = a and x = b?

Why “signed” area? How do we calculate it? What does it represent?

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.

Consider the graph of y = f(x) below. Find: (a) (b) (c) (d)

Find by using the definition.

The following integral statements are true: 1. 2. 3. If a < c < b, then 4. 5.

Suppose Find:

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