This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 to 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€...
View
Full Document
 Spring '08
 Smith
 Calculus, Antiderivatives, Definite Integrals, Derivative, Fundamental Theorem Of Calculus, Integrals, Limits, Hanford High School, Greg Kelly

Click to edit the document details