${\displaystyle \underset{3}{\overset{4}{}}}\sqrt[\phantom{2}]{x^3-27}dx,n=10$

$(a)$ the Trapezoidal Rule

$(b)$ the Midpoint Rule

$(c)$ Simpson's Rule

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule $to$ approximate the given integral with the specified value $ofn.(Round$ your answers $to$ six

decimal places.$)$

${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}\sqrt[3]{1+cos(x)}dx,n=4$

$(a)$ the Trapezoidal Rule

$(b)$ the Midpoint Rule

$(c)$ Simpson's Rule