Chapter 4: Q. 5 (page 403)

Fill in the blanks to complete each of the following theorem statements:
5. The Mean Value Theorem for Integrals: If $f$ is __ on $[a, b]$ , then there is some $c \in_$ such that $f (c) =___$

Short Answer

Expert verified

If $f$ is continuous on localid="1648819690172" $[a, b]$ , then there is some localid="1648819685981" $c \in (a, b)$ such that

localid="1648819693390" $f (c) = \frac{1}{b - a} \int_{a}^{b} f (x) d x$

Step by step solution

Step 1. Given data

We have to fill the blank space,

The Mean Value Theorem for Integrals: If $f$ is ____ on $[a, b]$ , then there is some role="math" localid="1648816458595" $c \in____$ such thatrole="math" localid="1648816452680" $f (c) =____$

Step 1. Fill in the blacks

If $f$ is continuous on a $[a, b]$ , then there is some $c \in (a, b)$ such that $f (c) = \frac{1}{b - a} \int_{a}^{b} f (x) d x$

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Fill in the blanks to complete each of the following theorem statements:
5. The Mean Value Theorem for Integrals: If $f$ is __ on $[a, b]$ , then there is some $c \in_$ such that $f (c) =___$

Short Answer

Step by step solution

Step 1. Given data

Step 1. Fill in the blacks

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Fill in the blanks to complete each of the following theorem statements:5. The Mean Value Theorem for Integrals: If fis ____ on [a,b], then there is some c∈___such that f(c)=___

Short Answer

Step by step solution

Step 1. Given data

Step 1. Fill in the blacks

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Fill in the blanks to complete each of the following theorem statements:
5. The Mean Value Theorem for Integrals: If $f$ is __ on $[a, b]$ , then there is some $c \in_$ such that $f (c) =___$