Compute

I $=$

Z $\backslash$pi

$2$

$0$

x

$1\mathrm{.}5$

cos$($x

$2$

$)$ dx

using the methods requested below. Parts $($a$)$ through $($d$)$ must be done by hand; you can use

Python to help with calculations if you do not use any of the numerical integration libraries:

$($a$)(2$ pts$)$ Trapezoid rule using $4$ equal$-$sized panels of width h $=$

$\backslash$pi

$8$

on the interval $[0,$

$\backslash$pi

$2$

$]$

$($b$)(2$ pts$)$ Midpoint rule using the midpoints of the panels described in part $($a$)$

$($c$)(2$ pts$)$ Trapezoid rule with end correction using the same $4$ panels

$($d$)(2$ pts$)$ Simpson$$s rule using the same $4$ panels $($use $2$ Simpson panels of size $$Simpson $=2$h$,$

where h is the grid spacing of the panels from part $($a$)).$

$($e$)(2$ pts$)$ Use scipy.integrate.quad with default error tolerances to compute the integral.

Which of your answers in parts $($a$)$ through $($d$)$ most closely matches the value computed

here?