Thin rod nonuniform linear mass density

[Talltunetalk]

Homework Statement

A thin rod of total length L has a nonuniform density given by λ(x)=ae^-bx where x is distance from one end of the rod. What is the moment of inertia of the rod for rotations around the end at x=0. Measuring from x=0 to x=L

Homework Equations

λ(x)=ae^-bx
Inertia=I=∫dmr^2
dm=λ(x)dx
r=x
I=mr^2

The Attempt at a Solution

my answer is -e^(bL)a[L^2/b + 2L/b^2 + 2/b^3] + 2a/b^3

I do not think this is correct because my units are not in mass*length^2

 

[ehild]

It looks correct. a and b mus have dimensions. a is linear density, [a]=[mass]/[length] and =1/[length].

ehild