A homogeneous wire is bent into the shape shown. Determine the $x$ coordinate of its centroid by direct integration. Express your answer in terms of a$.$

Multiple Choice

$\stackrel{}{x}=0\mathrm{.}746a$

$\stackrel{}{x}=0\mathrm{.}446a$

$$

$\stackrel{}{x}=0\mathrm{.}646a$

$\stackrel{}{x}=0\mathrm{.}546a$