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## Homework Statement

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.

## Homework Equations

[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]

=[itex]\frac{3x^4}{4}[/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.