OPERASI TURUNAN DAN INTEGRAL PADA MATLAB JURNAL PRAKTIKUM
Oleh : JULIA EKA EK A PUTRI AYUNINGTYAS YUNINGTYAS NIM : 151810401054 151810401054
LABORATORIUM MATEMATIKA JURUSAN MATEMATIKA FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM UNIVERSITAS JEMBER TAHUN TAHUN 015 0 15
BAB 1 PENDAHULUAN
1.1 Latar Belakang K!l"#l#$ %e%&l&"& '#! (!)!*+ #,!%!- "!l"#l#$ '&.e/e*$&!l '!* "!l"#l#$
&*,e+/!lT2&" #,!%! "!l"#l#$ '&.e/e*$&!l 3!&,# ,#/#*!* T#/#*!* %e%2#*3!& !2l&"!$&
'!l!%
'&"e%)!*+"!*
$e%#! %e*3#$#l
)&'!*+ "#!*,&,!,&. '&"e%)!*+"!**3!
Ke%#'&!* %!$!l!h
"!l"#l#$ &*,e+/!l '!l!%
'&.e/e*$&!$&
$eh&*++! %!,e%!,&"!!* h!/#$ )e/2&"&/ )!+!&%!*! %e*3ele$!&"!* %!$!l!h 3!*+ )e/"e)!l&"!* 'e*+!* $l#$& '&.e/e*$&!$& T#/#*!* '!* &*,e+/!l %e*!'& 2e/!*!* 2e*,&*+ '!l!% "!l"#l#$- 'e*+!* )e/)!+!& %!(!% !2l&"!$& 2!'! $!&*$ '!* ,e"*&" h&*++! )&'!*+ e"*%& A2l&"!$& "!l"#l#$ &*,e+/!l %el&2#,& 2e/h&,#*+!* l#!$6l#%e- 2!*!*+ )#$#/- 2#$!, %!$$!- "e/!- '!* ,e"!*!* Se'!*+"!* !2l&"!$& '!/& "!l"#l#$ '&.e/e*$&!l %el&2#,& 2e/h&,#*+!* "e(e2!,!* '!* 2e/(e2!,!*- "e%&/&*+!* $#!,# "e/6!- *&l!& %&*&%#% '!* %!"$&%#% T#/#*!* '!* &*,e+/!l %e%&l&"& 2e/h&,#*+!* 3!*+ ,&'!" $e'&"&, '!* /#%&, '&)!*'&*+"!* 2e/!$& h&,#*+!* %!,e%!,&"! l!&**3! B!*3!" 2e/%&$!l!* 7 %&$!l!* 3!*+ '&+#*!"!* #*,#" %e*3ele$!&"!* 2e/!$& h&,#*+!* ,#/#*!* '!* "h#$#$*3! &*,e+/!l O2e/!$& h&,#*+!* &*,e+/!l '!* ,#/#*!* &"! '&$ele$&"!* 'e*+!* (!/! %!*#!l !"!* %e%!"!* !",# 3!*+ l!%! leh "!/e*! &,# '&+#*!"!*l!h !2l&"!$& M!,l!) A2l&"!$& M!,l!) !"!* %e*3ele$!&"!* 2e/h&,#*+!* ,e*,!*+ ,#/#*!* '!* &*,e+/!l 'e*+!* (e2!, '!* le)&h %#'!h 1.2 Rumusan Masala 11 B!+!&%!*! 2e*+2e/!$&!* &*,e+/!l '!l!% M!,l!) 1 B!+!&%!*! 2e*+2e/!$&!* ,#/#*!* '!l!% M!,l!) 1.! Tu"uan 191 Me*+e,!h#& (!/! %e*3ele$!&"!* 2e/!$& &*,e+/!l 2!'! M!,l!) 19 Me*+e,!h#& (!/! %e*3ele$!&"!* 2e/!$& ,#/#*! 2!'! M!,l!) 1.# Man$aat 141 Pe%)!(! %e*+e/,& (!/! %e*3ele$!&"!* 2e/!$& &*,e+/!l 2!'! M!,l!) 14 Pe%)!(! %e*+e/,& (!/! %e*3ele$!&"!* 2e/!$& &*,e+/!l 2!'! M!,l!) BAB 2 TIN%AUN PUSTA&A 2.1 O'eras( Integral )alam Matla* I*,e+/!l 'e*+!* )!,!$ ,e/,e*,# !,!# l#!$ '!e/!h '&)!!h "#/6! '!l!%
/!*+e 3!*+ .&*&,&6e '!2!, '&,e*,#"!* 'e*+!* ,&+! )#!h .#*+$& 3!*+ '&%&l&"&
%!,l!) 3!&,# : ,/!2- ;#!'- ;#!'8 F#*+$& ,/!2 %e*'e"!,& &*,e+/!l 'e*+!* %e,'e ,/!2e$%- $e'!*+"!* ;#!' )e/'!$!/ 2!'! %e,'e ;#!'/!,#'e I*,e+/!l )&!$!*3! '&'e.&*&$&"!* $e)!+!& 2/$e$ 2e*#%l!h!* ,e,!2& #+! '&&*,e/2/e,!$&"!* $e)!+!& '!e/!h '&)!!h "#/6! 3 ? .<@> '!/& ! "e )
'!e/!h '&!,!$ @ '&h&,#*+ 2$&,&. $e%e*,!/! '&)!!h @ '&h&,#*+ *e+!,&. B!*3!" %e,'e *#%e/&" #*,#" &*,e+/!$& '&'!$!/"!* 2!'! &%2/e,!$& #*,#" %e*'!2!,"!* !2/"&%!$& &*,e+/!l*3! M&$!l*3! .#*+$& ,/!2 )e/'!$!/"!* &%2/e,!$& )!*+#*!* ,/!2e$%
*,h 2e/h&,#*+!* &*,e+/!l 'e*+!* )e/)!+!& %e,'! *#%/&" #*,#" %e*+h&,#*+ &*,e+/!l .#*+$& Pe/,!%! "&,! )#!, '#l# .#*+$& '!/& 2e/$!%!!* '&!,!$ .#*(,&* 3?h#%2$<@> 3?1=<@9>C01>1=<<@>C04> 1 Me*+&,#*+ %e*++#*!"!* ,/!2 @?1:1: 3?h#%2$<@> !/e!?,/!2<@-3> !/e! ? 145 Me*+h&,#*+ %e*++#*!"!* ;#!' @?1:1: 3?h#%2$<@> !/e!?;#!'<h#%2$-1-> !/e! ? 1104 Be/&"#, T!)el .#*+$& 7 .#*+$& 3!*+ '&+#*!"!* 2!'! M!,l!) '!l!% 2e/h&,#*+!* &*,e+/!l )e$e/,! "e+#*!!*3! F#*+$& ,/!2<@-3>
,/!2<@-A>
Ke+#*!!* %e*+h&,#*+ &*,e+/!l '!/& 3 $e)!+!& .#*+$& '!/& @ Ve",/ @ '!* 3 2!*!*+*3! h!/#$ $!%! N&l!& ele%e* '!l!% @ $e)!&"*3! '&$/,&/ %e*+h&,#*+ &*,e+/!l '!/& $e,&!2 "l% '& A $e)!+!& .#*+$& '!/& @ h!$&l*3! )e/#2! 6e",/
)!/&$ )e/&$& h!$&l &*,e+/!$& J#%l!h "l% A h!/#$ $!%! 'e*+!* 2!*!*+ @ ,/!2<@-A> %e*+h&,#*+ !2/"$&%!$& '!/& &*,e+/!l .#*+$& .(* 2!'! &*,e/6!l ! @ ) F#*+$& .(* h!/#$ '&'e.&*&$&"!* ,e/le)&h '!h#l# '!l!% M.&le ;#!'<.(*-!-)-,l> %e*+h&,#*+ !2/"$&%!$& &*,e+/!l '!/& .(* 'e*+!* ,le/!*$& "e$!l!h!* $e)e$!/ ,l ;#!'<.(*-!-)-,l-,/!(e-2&(> %e*+h&,#*+ !2/"$&%!$& &*,e+/!l '!/& .(* 'e*+!* ,le/!*$& ,l J&"! ,/!(e ,&'!" *l%!"! +/!.&" 3!*+ %e*+&l#$,/!$&"!* &*,e+/!l !"!* '&2l, H!$&l &*,e+/!$& '&e6!l#!$& 2!'! 2&( )&$! '&)e/& *&l!& *l 2!'! ,l '!* ,/!(e 'e*+!* %!,/&"$ "$*+ ;#!'l< > $!%! 'e*+!* (%%!*' ;#!'- ,e,!2& %e*+h&,#*+ 'e*+!* !"#/!$& 3!*+ le)&h ,&*++& 2.2 O'eras( Turunan )alam Matla* Me*e*,#"!* ,#/#*!* .#*+$& $e(!/! !*!l&,&" %#*+"&* %e*3#l&,"!* %e$"&2#* /el!,&. l!*+$#*+ Pe%)!l&"!* '!/& 2/$e$ &*& !"!* %e*e*,#"!* &*,e+/!l .#*+$&- ,!2& le)&h $e/&*+ $#l&, &"! $e(!/! !*!l&,&" !,!# )!h"!* ,&'!" %#*+"&* D!l!% M!,l!)- '&.e/e*$&!l #*,#" .#*+$& 2l&*% !'!l!h /el!,&. %#'!h M&$!l*3! .<@> ? @5 @4 5@ @ 9 %!"! !%)&l!h "e.&$&e* "e.&$&e**3! *,h: +?1 5 9 +? 159 h?2l3'e/<+> h? 4 10 Be*,#")e*,#" 'e.e/e*$&!l l!&* #+! )&$! '&2e/leh !2!l!+I &"! %e*++#*!"!* $3%)l3( %!,h ,l)@ T!2& ,&'!" $e,&!2 %!,l!) '&le*+"!2&
'e*+!* ,l)@ &*& N!%#*
h!l &,# ,&'!" %!$!l!h- 2e*3ele$!&!* '!2!,
'e*+!* %e%!*.!!,"!* 'e/e, T!3l/ D&.e/e*$&!l N#%e/&" : .#*(,&* ;?'&..+e*<.#*(-*-@-h> &. <<*?1><*??><*??9><*??4>> (?e/$<4-> (<1-:>? 0 1 8 0 8 1 0 (<-:>?0 1 1 90 1 1 0 (<9-:>?15 1 15 0 15 1 15 (<4-:>? 4 8 11 8 4 3?.e6!l<.#*(-@ 9:9Qh> ;?(<*-:>Q3 ; ? ;=<1QhC*> el$e '&$2<* h!/#$ 1- - 9 !,!# 4 >)/e!" e*' Pe*++#*!!* .#*+$& '&!,!$: J&"! "&,! %e%2#*3! 3 ? ($<@> '!* "&,! !"!* %e*+h&,#*+ ,#/#*!* "e'#! 'e*+!* @ ? 1 'e*+!* h !,!# "e,el&,&!* 001 %!"! '&,#l&$"!*: h!$&l?'&..+e*<($--1-01> h!$&l ? 094 J&"! "&,! &*+&* %e*+h&,#*+ $e)#!h '&.e/e*$&!l '&$#!,# ,&,&" %!"! "&,! h!/#$ %e*'e.&*&$&"!* .#*+$&*3! ,e/le)&h '!h#l#
BAB ! METODOLOGI !.1 Alat L!2,2 A(e/ A$2&/e E 14 !.2 Baan A2l&"!$& M!,l!) R00! Ne
DA+TAR PUSTA&A
He/*!!,&- K#$!/& H!*'#, A2l&"!$& K%2#,e/ J#/'&" M!,e%!,&"! FMIPA UNY2'. UNIKOM00 D&",!, M!,l!) S&%#l&*" &,h A22l&(!,&* J#/#$!* Te"*&" Ele",/: U*&6e/$&,!$ K%2#,e/ I*'*e$&! T#,/&!l M!,l!)2'. D&!"$e$ 2!'! !l"!,el!"!/,!ee)l3(% 2!'! ,!*++!l O",)e/ 015