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Part $1$

The difference between the true value $ofan$ integral and the value given $by$ the trapezoidal rule $or$ Simpson's rule $is$ known $as$ the error. $In$ numerical analysis, the error $is$ studied $to$ determine how large $n$ must $be$ for the error $tobe$ smaller than some specified amount. For both rules, the error $is$ inversely proportional $to$ a power $ofn,$ the number $of$ subdivisions. $In$ other words, the error $is$ roughly

StartFraction $k$ Over $n$ Superscript $p$ EndFraction

where $kis$ a constant that depends $on$ the function and the interval, and $pis$ a power that depends only $on$ the method used. With a little experimentation, you can find out what the power $pis$ for the trapezoidal rule and for Simpson's rule. Complete parts $a.$ through $c.$ below.

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Part $1$

$a.$ Find the exact value $of$

Integral from $0to17x$ cubed font size decreased $by6dx.$

Integral from $0to17x$ cubed font size decreased $by6$ dxequalsenter your response here

$(Typean$ integer $or$ a decimal.$)$