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5.5 Properties of the Definite Integral
Rita Korsunsky
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Property: Definite Integral of a Constant Function
If is a real number, then .
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Proof is based on the fact that limit of the sum is equal to sum of the limits.
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Simplify
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Total area = sum of areas
a c b
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By the above theorem
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Mean Value Theorem for Definite Integrals
If is continuous on a closed interval , then there is a number in the open interval such that .
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Average Value of a Function
If is continuous on a closed interval , then the average value of on is .
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Average Value of a Function
Yielding the general form:
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