Consider the shaded area in $($Figure $1).$ Take $L=1\mathrm{.}4m.$

Figure

Part A

Locate the centroid $\stackrel{}{x}$ of the area. Solve the problem by evaluating the integrals using vertical differential area strips and

Simpson's rule ${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$~~$\frac{b-a}{6}[f(a)+4f(\frac{a+b}{2})+f(b)].$

Express your answer to three significant figures and include the appropriate units.