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SCALCET$97\mathrm{.}7\mathrm{.}008.$

Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral with the specified value of $n.($Round your answers to six decimal places.$)$

${\displaystyle \underset{5}{\overset{8}{}}}sin(\sqrt[\phantom{2}]{x})dx,n=6$

$($a$)$ the trapezoidal rule

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$\mathrm{.}133131$

$($b$)$ the midpoint rule

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$($c$)$ Simpson's rule

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