The linear density rho in a rod 3 m long is 9/ x + 1 kg/m, where x is measured in meters from one end of the rod. Find the average density rhoave of the rod.

Respuesta :

Answer: 4.29 kg/m

Explanation:The average density could be calculated by taking the integral of the rho function and dividing it by length of the rod

The integral function sums up all the density and then dividing by length gives us the average density

[tex]rho_a=\frac{1}{3} \int\limits^3_0 {9/x +1} \, dx \\rho_a=(9ln x +x)/3\\rho_a=(9ln3+3)/3\\rho_a=4.29 kg/m[/tex]