2. (Mean Value Theorem for Integrals) If f(x) is continuous over an interval [a, b], then there is at least one point x = c in [a, b] such that 9 f(x) = 3. (0) = 6 -²- af f(xdx For the following functions, find the value(s) of x = c that's guaranteed by the Mean Value theorem for integrals. f(x) = sin(x), [0, π] [1,3] f(c) =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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2. (Mean Value Theorem for Integrals) If ƒ(x) is continuous over an interval [a, b], then there is at least
one point x = c in [a, b] such that
1
f(0) = 6²a²f(x)dx
b-a
For the following functions, find the value(s) of x = c that's guaranteed by the Mean Value theorem for
integrals.
f(x) = sin(x),
9
f(x) = -3₁
[1,3]
Transcribed Image Text:2. (Mean Value Theorem for Integrals) If ƒ(x) is continuous over an interval [a, b], then there is at least one point x = c in [a, b] such that 1 f(0) = 6²a²f(x)dx b-a For the following functions, find the value(s) of x = c that's guaranteed by the Mean Value theorem for integrals. f(x) = sin(x), 9 f(x) = -3₁ [1,3]
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