# 1314L20 - Lesson 20 Evaluating Definite Integrals We will...

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Lesson 20 – Evaluating Definite Integrals 1 Lesson 20 Evaluating Definite Integrals We will sometimes need these properties when computing definite integrals. Properties of Definite Integrals Suppose f and g are integrable functions. Then: 1. 0 ) ( = a a dx x f 2. - = a b b a dx x f dx x f ) ( ) ( 3. = b a b a dx x f c dx x cf ) ( ) ( 4. ± = ± b a b a b a dx x g dx x f dx x g x f ) ( ) ( )] ( ) ( [ 5. < < + = b a b c c a b c a dx x f dx x f dx x f where ) ( ) ( ) ( We will need to use substitution to evaluate some problems: Example 1: Evaluate ( 29 - 2 0 3 2 1 2 dx x x

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Lesson 20 – Evaluating Definite Integrals 2 Example 2: Evaluate ( 29 - 3 0 5 2 3 4 dx x x Example 3: Evaluate 1 0 2 3 dx e x x
Lesson 20 – Evaluating Definite Integrals 3 Example 4: Evaluate + 2 1 3 2 6 3 dx x x Example 5: Evaluate + 1 0 1 2 1 dx x

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Lesson 20 – Evaluating Definite Integrals 4 Applications Example 6: A company purchases a new machine for which the rate of depreciation is
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1314L20 - Lesson 20 Evaluating Definite Integrals We will...

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