The linear density rho in a rod 3 m long is 15 / square root {x + 1} kg/m, where x is measured in...


The linear density {eq}\rho {/eq} in a rod {eq}3\:m {/eq} long is {eq}15/\sqrt{x+1}\:kg/m {/eq}, where {eq}x {/eq} is measured in meters from one end of the rod. Find the average density {eq}\rho_{ave} {/eq} of the rod.

Average value

The average value of a function f(x) over the interval (a, b) is

{eq}\displaystyle f_{avg}(x) = \frac{\int_a^b f(x)dx}{b - a} {/eq}

This is so because the defnite integration of a function over a period is simply the addition of the values of function over the time.

Answer and Explanation:

Given linear density rho is {eq}\displaystyle f(x) = 15{x + 1}^{\frac{1}{2}} {/eq}

The time is between 0 to 3 meters

So the average value of...

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Learn more about this topic:

Law of Averages: Definition & Formula

from General Studies Math: Help & Review

Chapter 5 / Lesson 8

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