LarCalcET$88\mathrm{.}6\mathrm{.}027.$

Consider the error formulas.

$|$E$|$

$($b $$ a$)312$n$2$

$[\backslash$pre$\{$max$\{|$f$($x$)|],$a $$ x $$ b

$$Trapezoidal Rule

$|$E$|$

$($b $$ a$)5180$n$4$

$[$max $|$f$(4)($x$)|],$a $$ x $$ b

$$Simpson$\text{'}$s Rule

Use these to estimate the errors in approximating the integral, with n $=4,$ using the Trapezoidal Rule and Simpson's Rule.

$4$

$1($x $1)2$

$$dx$2$

$($a$)$

Trapezoidal Rule

$($b$)$

Simpson's Rule