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Problem 26 Hard Difficulty
If $ f_{ave} [a, b] $ denotes the average value of $ f $ on the interval $ [a, b] $ and $ a < c < b $, show that
$$ f_{ave} [a, b] = \frac{c - a}{b - a} f_{ave} [a, c] + \frac{b - c}{b - a} f_{ave} [c, b] $$
Answer
$f_{a v e}[a, b]$
Topics
Applications of Integration
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Top Calculus 2 / BC Educators
Anna Marie V.
Campbell University
Heather Z.
Oregon State University
Michael J.
Idaho State University
Joseph L.
Boston College
Watch More Solved Questions in Chapter 6
Video Transcript
we know the average value formula could be written with a beak, A, C and C B. Therefore, we know C minus a over B minus a times one over C minus A from a C. Kovacs detox is equivalent to one over B minus A from A to C of after box detox. And we know this can also be written as one over B minus a from sea to be after Rex detox. Given the fact that we are looking at the interval from A to B, we know we can write this as won over B minus A from A to B aftereffects. Detox is equivalent to the average value from A to B.
Topics
Applications of Integration
Top Calculus 2 / BC Educators
Anna Marie V.
Campbell University
Heather Z.
Oregon State University
Michael J.
Idaho State University
Joseph L.
Boston College