Give $an$ inequality comparing $\frac{1}{\sqrt[\phantom{2}]{x}}$ and $\frac{|sin(x)|}{\sqrt[\phantom{2}]{x}}$ for ${\displaystyle \underset{0}{\overset{1}{}}}\frac{|sin(x)|}{6\sqrt[\phantom{2}]{x}}dx0.$

$(Express$ numbers $in$ exact form. Use symbolic notation and fractions where needed.$)$

inequality:

Use this inequality $to$ determine whether the integral ${\displaystyle \underset{0}{\overset{1}{}}}\frac{|sin(x)|}{6\sqrt[\phantom{2}]{x}}dx$ converges.