Consider the integral $\backslash (\backslash$int$\_\{0\}^\{5\}\backslash$sin $(3\backslash$pi t$)$ d t $\backslash )$

Use the Trapezoidal Rule with $\backslash ($ n$=4\backslash )$ to approximate the integral:

The integral is approximately

Find the best upper bound for the error in your approximation using the error estimate formula:

$\backslash [$

$\backslash$left$|$E$\_\{$T$\}\backslash$right$|\backslash$leq

$\backslash ]$

Calculate the actual value of the integral, and use this to calculate the error in your approximation:

$\backslash [$

$\backslash$left$|$E$\_\{$T$\}\backslash$right$|=$

$\backslash ]$

Now calculate the percent error in your approximation by dividing the error by the actual value of the integral, then multiplying by $100$:

Percent error is

Now use Simpson's Rule with $\backslash ($ n$=4\backslash )$ to approximate the original integral:

The integral is approximately

Find the best upper bound for the error in your approximation using the error estimate formula:

$\backslash [$

$\backslash$left$|$E$\_\{$S$\}\backslash$right$|\backslash$leq

$\backslash ]$

Calculate the actual value of the integral, and use this to calculate the error in your approximation:

$\backslash [$

$\backslash$left$|$E$\_\{$S$\}\backslash$right$|=$

$\backslash ]$

Now calculate the percent error in your approximation by dividing the error by the actual value of the integral, then multiplying by $100$:

Percent error is