Calc05_3 - subtracted. 5. ( 29 ( 29 ( 29 b c c a b a f x dx...

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5.3 Definite Integrals and Antiderivatives Greg Kelly, Hanford High School, Richland, Washington
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Page 269 gives rules for working with integrals, the most important of which are: 2. ( 29 0 a a f x dx = If the upper and lower limits are equal, then the integral is zero. 1. ( 29 ( 29 b a a b f x dx f x dx = - Reversing the limits changes the sign. ( 29 ( 29 b b a a k f x dx k f x dx = 3. Constant multiples can be moved outside.
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1. ( 29 0 a a f x dx = If the upper and lower limits are equal, then the integral is zero. 2. ( 29 ( 29 b a a b f x dx f x dx = - Reversing the limits changes the sign. ( 29 ( 29 b b a a k f x dx k f x dx = 3. Constant multiples can be moved outside. ( 29 ( 29 ( 29 ( 29 b b b a a a f x g x dx f x dx g x dx + = + 4. Integrals can be added and subtracted.
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( 29 ( 29 ( 29 ( 29 b b b a a a f x g x dx f x dx g x dx + = + 4. Integrals can be added and
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Unformatted text preview: subtracted. 5. ( 29 ( 29 ( 29 b c c a b a f x dx f x dx f x dx + = Intervals can be added (or subtracted.) a b c ( 29 y f x = The average value of a function is the value that would give the same area if the function was a constant: 2 1 2 y x = 3 2 1 2 A x dx = 3 3 1 6 x = 27 6 = 9 2 = 4.5 = 4.5 Average Value 1.5 3 = = ( 29 Area 1 Average Value Width b a f x dx b a = =- 1.5 The mean value theorem for definite integrals says that for a continuous function, at some point on the interval the actual value will equal the average value. Mean Value Theorem (for definite integrals) If f is continuous on then at some point c in , [ ] , a b [ ] , a b ( 29 ( 29 1 b a f c f x dx b a =-...
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Calc05_3 - subtracted. 5. ( 29 ( 29 ( 29 b c c a b a f x dx...

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