Chapter 4, Problem 53RE

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Using the Mean Value Theorem for Integrals In Exercises 53 and 54, find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f ( x ) = 3 x 2 ,             [ 1 ,   3 ]

To determine

To calculate: The value(s) of c for the integrals f(x)=3x2,[1,3] over the given intervalusing the Mean Value Theorem.

Explanation

Given:

f(x)=3x2,â€‰â€‰â€‰[1,3]

Formula used:

Mean value theorem: If any function is differentiable and continuous in a given interval [a,b] then,

fâ€²(c)=f(b)âˆ’f(a)bâˆ’a

Calculation:

We will use the mean value theorem for the integral there must exists some câˆˆ[1,3] such that

âˆ«13f(x)dx=f(c)(3âˆ’1)

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