# The linear density in a rod 10 meters long is \frac{8}{\sqrt{x+4}} , where x is measured in...

## Question:

The linear density in a rod 10 meters long is {eq}\frac{8}{\sqrt{x+4}} {/eq}, where {eq}x {/eq} is measured in meters from one end of the rod. Find the average density of the rod.

## Average density of a Function:

find total mass of the rod by integration . Then divide this total mass by total length of the rod to get the average density of the rod

## Answer and Explanation:

Linear mass density is {eq}\rho(x)=\frac{8}{\sqrt{x+4}} {/eq}

Mass of small element of the rod of length dx is

{eq}dm=\rho(x) dx {/eq}

{eq}dm=\fr...

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Law of Averages: Definition & Formula

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