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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 + = âˆ« âˆ« âˆ« Intervals can be added (or subtracted.) a b c ( 29 y f x = â†’ 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 = âˆ« 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 = =-âˆ« 1.5 â†’ 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 =-âˆ« Ï€...

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