MATH 2B Chapter Notes - Chapter 6.5: Riemann Sum, Mean Value Theorem

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: George Donaldson

Document Summary

Recall the usual meaning of average: if we have a collection of n values y1, . , yn, then its average is yav = y1 + + yn n. = (b a) f (x 1) + + f (x n) n. This motivates us to de ne the notion of average for any integrable function. The average value of a function f over [a, b] is fav = A z b a f (x) dx. To visualize the average value, imaging a bull- dozer attening out all the peaks of a function and pushing the debris into its troughs. The result is a rectangle with height fav. Otherwise said, the blue and gray areas are identical. y fav. Note that if f is a constant function f (x) = c, then the average value is simply a fav = A z b a c dx = A (b a)c = c x b.