Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the glven Interval. f(x) = cos(x), Step 1 Recall that the Mean Value Theorem Is stated as follows. If f is continuous on the closed Interval (0, b], then there exists a number c In the closed Interval [a, b] such that f(x) dx = f(c)(b - 0). In terms of area, this means there is a rectangle with side lengths (c) and (b - a) that has the same area as found by f(x) dx.
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the glven Interval. f(x) = cos(x), Step 1 Recall that the Mean Value Theorem Is stated as follows. If f is continuous on the closed Interval (0, b], then there exists a number c In the closed Interval [a, b] such that f(x) dx = f(c)(b - 0). In terms of area, this means there is a rectangle with side lengths (c) and (b - a) that has the same area as found by f(x) dx.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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![Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the glven Interval.
f(x) = cos(x),
Step 1
Recall that the Mean Value Theorem Is stated as follows.
If fis continuous on the closed Interval [0, b], then there exists a number c In the closed Interval [a, b] such that
f(x) dx = f(c)(b - a).
In terms of area, this means there Is a rectangle with side lengths (c) and (b -a) that has the same area as found by
f(x) dx.
We are glven the function f(x) = cos(x) and the Interval
The function f(x) is
v continuous on the given Interval. Therefore, we must find the value of c In
that makes the following equation true.
cos(x) dx = cos(c)
/3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc366fd3b-620f-474a-a6bd-a20dc9199f80%2F69839b12-b518-42e0-a59b-061f2fc2136f%2Fulxqo2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the glven Interval.
f(x) = cos(x),
Step 1
Recall that the Mean Value Theorem Is stated as follows.
If fis continuous on the closed Interval [0, b], then there exists a number c In the closed Interval [a, b] such that
f(x) dx = f(c)(b - a).
In terms of area, this means there Is a rectangle with side lengths (c) and (b -a) that has the same area as found by
f(x) dx.
We are glven the function f(x) = cos(x) and the Interval
The function f(x) is
v continuous on the given Interval. Therefore, we must find the value of c In
that makes the following equation true.
cos(x) dx = cos(c)
/3
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