Question

A rod of length 3 meters with density 1+x^2 g/m is positioned along with positive x-axis, with its left end at the origin. Find the total mass and the center of mass of the rod.

Answer 1

Mass = Density * Length (for a linear object)
Center of mass is at the center of the entire length of the linear object.

Answer 2

\[\large mass = \int\limits_0^3 (1+x^{2}) dx\]
center of mass is at point on rod where equal mass is on either side
let "m" be center of mass
\[\large \int\limits_0^m (1+x^{2}) dx = \frac{1}{2}mass\]