$($b$)$ Evaluate the definite integral using the limits obtained by trigonometric substitution. $($Remember to use absolute values where appropria

$\{\begin{array}{c}\text{:}{\displaystyle \underset{2}{\overset{4}{}}}\frac{\sqrt[\phantom{2}]{x^2-16}}{x^2}dx=[x{]}_0^{\frac{}{3}}\end{array}$