   Chapter 4.4, Problem 49E

Chapter
Section
Textbook Problem

Using the Mean Value Theorem for Integrals In Exercises 47-52, find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. y = x 2 4 ,         [ 0 , 6 ]

To determine

To calculate: The values of c in the interval [0,6] for the function y=x24 for which the Mean Value Theorem for Integrals holds.

Explanation

Given:

The function y=x24 and the interval [0,6].

Formula Used:

The Mean Value Theorem for integrals states that for function f that is continuous over a closed interval [a,b], there exists a c in the interval such that:

abf(x)dx=f(c)(ba)

Calculation:

First calculate the anti-derivative of the function over the provided domain

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