Answered: Estimate the average value of the…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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Question

Estimate the average value of the function ƒ(x) = sin x on the interval
[0, π].

Expert Solution

Step 1

we have to find the average value of the function ƒ(x) = sin x on the interval
[0, π].

Step 2

$A s w e k n o w t h a t t h e a v e r a g e v a l u e o f t h e f u n c t i o n : A v e r a g e v a l u e = \frac{\int_{0}^{π} \sin x d x}{π - 0} A v e r a g e v a l u e = \frac{\int_{0}^{π} \sin x d x}{π} A v e r a g e v a l u e = \frac{{(- \cos x)}_{0}^{π}}{π} A v e r a g e v a l u e = \frac{- cosπ + \cos 0}{π} A v e r a g e v a l u e = \frac{1 + 1}{π} A v e r a g e v a l u e = \frac{2}{π}$

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