Definite Integral

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Definite Integral

• Suppose we want to evaluate an anti-
• derivative over some interval a, b in its
• domain. Then we need what is called a
• definite integral, denoted as

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How to evaluate?

• To evaluate a definite integral, we will use
• the Fundamental Theorem of Calculus

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Evaluate
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Evaluate
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Evaluate
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Evaluate
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• How is a definite integral different from an
• indefinite integral?
• How is a definite integral the same as an
• indefinite integral?

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What does a definite integral mean?

• A definite integral gives the net change in
• the value of an anti-derivative over some
• specified interval in the domain of the
• function.

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• Production costs of a new machine grow at
• a rate of 200vt dollars per week. Find the
• total production costs during the first month
• of production.
• Find the total production costs during the
• second month.

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Definition

• The average value of a function f(x) on
• an interval a, b is given by

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• For the previous production problem, find the
  average weekly costs during the first month
  during the first two months.

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On the TI-86

• Press 2nd
• Press F5 (fnInt)
• Enter (function, x, lower, upper)
• Press Enter

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On the TI-83

• Press MATH
• Select option 9
• Enter as (function, x, lower, upper)
• Press Enter