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2311lectureoutline5.4

# 2311lectureoutline5.4 - The integral of a rate of change is...

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MAC2311, Calculus I 5.4 Indefinite Integrals and the Net Change Theorem An antiderivative for f(x) can be referred to as an indefinite integral. The Indefinite Integral: ( ) ( ) f x dx F x = ° means ( ) ( ) F x f x = Example: The indefinite integral 2 5 (5 ) 2 x x dx C = + ° Notice that an indefinite integral is a family of functions, unlike a definite integral which equals a number. See the Table of Integrals. Net Change Theorem:
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Unformatted text preview: The integral of a rate of change is the net change: ( ) ( ) ( ) b a F x dx F b F a ′ =-& Example: If V(t) is the volume of water in a tank at time t, then its derivative V’(t) is the rate at which wate flows into the tank at time t. So 2 1 2 1 ( ) ( ) ( ) t t V x dx V t V t ′ =-& is the change in the amount of water in the tank between time t 1 and t 2 . Try exercises 6, 12, 16, 24, 28, 30, 34, 38, 50, 52, 60 on pages 397-398 in your text....
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