Calculate the moment of inertia of a uniform rigid rod of length L and mass M lying along the x-axis which rotates about an axis perpendicular to the rod (the y axis) and passing through it’s center of mass. The rod has a line density that is a function of location such that =3x.
[itex]\int ρr^2 dm[/itex]
The Attempt at a Solution
I thought this would be done simply by replacing ρ with 3x and r with x. However, while integrating I just keep getting 0 as my answer.
[itex]\int ρr^2 dm[/itex] dm=ρdx=3xdx
=[itex]\int 3x(x)^2 dx[/itex]
Now when I evaluate from L/2 and -L/2 I always get zero.
I assume I'm setting up my integral incorrectly as I should probably have an odd exponent that I totally forgot how to do calculate an integral over the summer. Appreciate the help.