Clas

Name:

Stwdent iDn

NOTE: $($i$)$ AVSWERS MUST IIF CLEARL YDERIVID.

$(2)$ OPEN BOOK, $(3)$ NO CELL PHONE AND NOINTERNET

$($a$)$ With the data given belon, eyaluate

${\displaystyle \underset{0}{\overset{26}{}}}f(x)dx$

by using $(1)$ the trapezoidal nile and $(2)$ Simpson's $\frac{1}{3}$ nule.

$\backslash$table$[[x,0,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}8,0\mathrm{.}5,0\mathrm{.}6],[f(x),03,0\mathrm{.}1,1\mathrm{.}2,0\mathrm{.}4,1\mathrm{.}8,1\mathrm{.}6,1\mathrm{.}2]]$

$($b$)$ Prave that $($:$f_i^{\text{'}}=\frac{-f_{i+1}+8f_{i-1}-R{f}_{i-1}+f_{i-2}}{12h}+O{h}^{-1}$