5.5 Properties of the Definite Integral

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Presentation transcript:

5.5 Properties of the Definite Integral Rita Korsunsky

Property: Definite Integral of a Constant Function If is a real number, then .

Proof is based on the fact that limit of the sum is equal to sum of the limits.

Simplify

Total area = sum of areas a c b

By the above theorem

Mean Value Theorem for Definite Integrals If is continuous on a closed interval , then there is a number in the open interval such that .

Average Value of a Function If is continuous on a closed interval , then the average value of on is .

Average Value of a Function Yielding the general form: