question about moment of inertia?

Question

A long thin rod lies along the x-axis from the origin to x=L, with L= 0.710 m. The mass per unit length, l (in kg/m) varies according to the equation l = l0 (1+1.110x3). The value of l0 is 0.300 kg/m and x is in meters.
Calculate the total mass of the rod.
Calculate the x-coordinate of the center of mass of the rod.
Calculate the moment of inertia of the rod with respect to the y-axis.

Answer 1

I set up the integral of
IO(1+1.110x^3) from 0 to L
and found the equation
m=.3*(x+.25*1.110*x^4)

using L=.710m
the mass is
.23 kg

and the center of mass is located where
m=.115kg

which calculates to be at
x=.3777 m

so the moment of inertia is:

.23*.3777

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