Linear Density & Center of Mass

[Ineedphysicshelp]

Would anyone be able to give me a hint for this question? Do I take the integral? I have possible answers but I am unsure.

A rod of length 30.0 cm has a linear density given by:

D = 50.0g/m + 20.0xg/m^2

where x is the distance from one end measured in meters. a. What is the mass of the rod. b. how far from the x=0 end is the center of mass?

 

[Astronuc]

Yes, you have to do the integration from 0 to 0.3 m.

Linear density (m') is mass/(unit length), so mass M = \int{m'(x)}\,dx.

 

[Tide]

You'll just integrate to find the mass:

M = \int_0^L D(x') dx'

and the center of mass is given by

x_{CM} = \frac {1}{M} \int_0^{L} x' D(x') dx'