Answer
$$m = 3$$
Work Step by Step
$$\eqalign{
& \rho \left( x \right) = 2 - \frac{x}{2},{\text{ }}0 \leqslant x \leqslant 2 \cr
& {\text{The mass of the object is }}m = \int_a^b {\rho \left( x \right)} dx,{\text{ }}\left( {{\text{See page 460}}} \right) \cr
& m = \int_0^2 {\left( {2 - \frac{x}{2}} \right)} dx \cr
& {\text{Integrating}} \cr
& m = \left[ {2x - \frac{{{x^2}}}{4}} \right]_0^2 \cr
& m = \left[ {2\left( 2 \right) - \frac{{{{\left( 2 \right)}^2}}}{4}} \right] - \left[ {2\left( 0 \right) - \frac{{{{\left( 0 \right)}^2}}}{4}} \right] \cr
& m = 3 \cr} $$
