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Lesson 20-filled

# Lesson 20-filled - Math 1314 Lesson 20 Evaluating Definite...

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Math 1314 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 ( - 3 0 5 2 3 4 dx x x

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Example 2 : Evaluate 1 0 2 3 dx e x x Example 3 : Evaluate 2 1 3 2 6 3 dx x x

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Applications Example 4 : A company purchases a new machine for which the rate of depreciation is given by ) 6 ( 000 , 10 - t . How much value is lost over the first three years that the machine is in use? Example 5 : Suppose you are driving a car and that your velocity can be approximated by 2 25 2 ) ( t t t v - = , where t is measured in seconds and v is measured in feet per second. How far will you travel in the 5 seconds from t = 0 to t = 5?

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