tugas invention sma sugar group

8/18/2019 Tugas invention SMA Sugar Group

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Amri Siddiq Pangestu, XII SCI C

SpV: Riana Hadiana

CALCULATING THE CERTAININTEGRAL BY USINGNUMERICAL TRAPEZOID

METHOD WITH R


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OUTLINECHAPTER I INTROUCTION


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CHAPTER I


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!AC"#ROUN$irst

Se%&nd

T'ird


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PRO!LE( $OR(ULATION


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O!)ECTIVE

To know


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CHAPTER II


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LITERATURE REVIE+eniti&neniti&n


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eniti&n


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T'e -&rmu.a &- a./a0ar1sintegrati&n

1

1

n na x x C n

+= ++∫

1

1

n nakx k x C n

+= ++∫


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T'e -&rmu.ati&n &- trig&n&metr21sintegrati&n

sin cos C θ θ = − +∫

cos sin C θ θ = +∫

1sin cos x x C α α

α = − +∫

1cos sin x x C α α

α

= +∫


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LITERATURE REVIE+eniti&neniti&n


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eniti&n


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Partiti&n


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Trapesium

[ ]0 12

h L y y= + [ ]2 1 2

2

h L y y= +


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T'e -&rmu.ati&n &- Numeri%a.trape3&id (et'&d

1 2( ) { ... }

b

nn

a

f x dx Lim L L L→∞

≡ + + +∫

0 1 11 2(y ) (y )(y )

( ) ...2 2 2

b

n n

na

h y h yh y

f x dx Lim −

→∞

+ ++ ≡ + + + ÷ ÷ ÷ ∫

0 1 1 2 2 1 1( ... y y( )2

b

n n n

na

h y y y y y y f x dx Lim − −

→∞

+ + + + + + + +≡∫

01 2 1( ) ( ... )

2 2

b

nn

na

y y f x dx Lim h y y y −→∞

≡ + + + + + ÷ ∫


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CHAPTER III


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(ETHOOLO#4

(a2 5678ILP "m 95


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(ETHOOLO#4PCPC


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PROCEURECa.%u.ate using numeri%a. trape3&id met'&d


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C&mparati&n


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CHAPTER IV


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ATA

NoFunction from the

book

The result from

the book

(analytical)

The result from numerical trapezoid method

n = 10 n = 100 n = 10000

1 0 1 0,3333333 0,33 0,3333 0,3333333

! ! " #$,####% #$,%! #$,##%! #$,####%

3 &1 ! 10, 10,#3 10,013 10,

" &1 0 &0, &0,"' 0,"''' &0,

&1 &0,''%'"3 &0,''''%'" &1

# 0 0, 0,"'$$0' 0,"'''$' 0,

% 0 0,1"!#''1 0,1"3!133 0,1"!%0"! 0,1"!#''1

2 x

24 x x−

32 1 x +

26 2 x x+ −

cos x

sin 5 cos 3 x x

2sin x

/ 2π

/ 2π

/ 4π

π

a b


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CHAPTER V


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CONCLUSION

T'e a%%urati&n is 766 t&t'e rea. resu.t 02 using

76666 partiti&n *it' t'eranges is 5,;,


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SU##ESTION

$ind t'e -&rmu.a t& %a.%u.atet'e .imit &- resu.t1s er&r, s&t'e 0&undar2 &- partiti&n1s

er&r %an 0e nd=


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!I!LIO#RAPH4 !e.., (a2, et= a.= 566>= Everyday Mathematics: Student

Re-eren%e !&&?s= (C#ra*@Hi..: United States &- Ameri%a

epartemen Pendidi?an Nasi&na.= 566. Kamus Besar BahasaIndonesia. Edisi

"etiga= !a.ai Pusta?a:)a?arta=#ra*,Hi..= 566;= Dictionary of Mathematics= Edisi "edua= T'eLa?eside Press: Ne* 4&r?=

"untarti, Su.isti2&n&, B"urnianingsi', S= 566= (atemati?a S(AUntu? "e.as XII Pr&gram I.mu A.am= #e.&ra A?saraPratama:)a?arta

Pesta dan An*ar= Matematika Aplikasi Untuk SMA dan MA Kelas

II !ro"ram Studi Ilmu Alam=Pusat Per0u?uan epartemenpendidi?an Nasi&na. :)a?arta=


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T'an? 4&u D

tugas invention sma sugar group

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