- #1

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## Homework Statement

I have a question can the average value for an integral be negative. I don't see why not just checking.

You know this evalutation f_ave = (1/b-a) ∫ f(x) dx

## Homework Equations

thx

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- Thread starter Jbreezy
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- #1

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I have a question can the average value for an integral be negative. I don't see why not just checking.

You know this evalutation f_ave = (1/b-a) ∫ f(x) dx

thx

- #2

pasmith

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## Homework Statement

I have a question can the average value for an integral be negative.

You know this evalutation f_ave = (1/b-a) ∫ f(x) dx

That is the average value of the function f on [a,b]. It can of course be negative, and will be if f(x) < 0 for all x in [a,b].

- #3

HallsofIvy

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If the average value of the function is negative, of course!## Homework Statement

I have a question can the average value for an integral be negative. I don't see why not just checking.

More correctly f_ave = (1/(b-a)) ∫ f(x) dx. What you wrote would normally be interpretedYou know this evalutation f_ave = (1/b-a) ∫ f(x) dx

f_ave = ((1/b)-a) ∫ f(x) dx

Of course. Take the simplest example: f(x)= -1 for all x.## Homework Equations

thxx

## The Attempt at a Solution

Then [tex]\int_0^1 f(x)dx= -\int_0^1 dx= -(1- 0)= -1[/tex]

Slightly more complicated, if f(x)= -x,

[tex]\int_0^1 f(x)dx= -\int_0^1 xdx= -\frac{1}{2}[/tex].

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