Обчислення визначеного інтеграла функції F(x) на відрізку [A,B] за формулою Сімпсона, Детальна інформація

Caeeoeiaee /eai ocaaaeueiaii? oi\x00F0ioee N\x00B3iiniia



Ca\x00B3aene ae\x00B3noa\x00BAii oaeo ioe\x00B3ieo aaniethoii? iioeaee /enaeueiiai \x00B3ioaa\x00F0oaaiiy ca ocaaaeueiaiith oi\x00F0ioeith N\x00B3iiniia :



sseui iaaeeaeaia cia/aiiy \x00B3ioaa\x00F0aea o\x00F0aaa ia/eneeoe c oi/i\x00B3noth (>0, a\x00B3aeiia\x00B3aeiee e\x00F0ie \x00B3ioaa\x00F0oaaiiy h aecia/a\x00BAoueny ia\x00F0\x00B3ai\x00B3noth

,

aai, ui oa naia, a\x00B3ae\x00F0\x00B3cie [a;b] o\x00F0aaa iiae\x00B3eeoe ia n \x00F0\x00B3aieo /anoei aea



Ca ocaaaeueiaiith oi\x00F0ioeith N\x00B3iiniia ia/eneeii iaaeeaeaia cia/aiiy \x00B3ioaa\x00F0aea (6.19) c e\x00F0ieii n=0,1 \x00B3 ioe\x00B3ieii iiaio aaniethoio iioeaeo (1.

Ei\x00F0enooth/enue oaaeeoeath 6.1, ca oi\x00F0ioeith (6.33) ciaeaeaii :

\x00B2ni=0,38177448(0,381745

Uia ioe\x00B3ieoe caeeoeiaee /eai R(f) oi\x00F0ioee N\x00B3iiniia ca oi\x00F0ioeith (6.35), o\x00F0aaa ciaeoe iio\x00B3aeio /aoaa\x00F0oiai ii\x00F0yaeeo a\x00B3ae ooieoe\x00B3? f(x)=xcosx, ia\x00BAii

f’’’’(x)=4sinx+xcosx, ca\x00B3aene





, a cia/aiiy i\x00B3ae\x00B3ioaa\x00F0aeueii? ooieoe\x00B3? f o aoceao Xk (k=0,1,...10) ia/enethaaee c oi/i\x00B3noth 0,5*10^(-7), oiaoi (f=0,5*10^(-7).

Ca oi\x00F0ioeith (6.3) aeey iiaii? aaniethoii? iioeaee /enaeueiiai \x00B3ioaa\x00F0oaaiiy ooieoe\x00B3? f(x)=xcosx ciaoiaeeii oaeo ioe\x00B3ieo :

((=0,278*10^(-5)+0,5*10^(-7)+0,2*10^(-7)=0,285*10^(-5)<0,3*10^(-5).

Ioaea ia/eneaia ca oi\x00F0ioeith N\x00B3iiniia aeey n=10,h=0,1 iaaeeaeaia cia/aiiy \x00B3ioaa\x00F0aea (6.19) ia\x00BA i’youe i\x00F0aaeeueieo cia/oueo cia/oueo oeeo\x00F0, oiaoi





Ia/eneeii \x00B3ioaa\x00F0ae (6.19) ca oi\x00F0ioeith (6.33), iieeaaoe n = 2, 4, 8, 16. Ciaeaeaii \x00B22 = 0,38182200; \x00B24=0,38177633; \x00B28=0,381773333. A oea icia/a\x00BA, ui \x00B22 ia\x00BA o\x00F0e, \x00B24 - i‘youe, \x00B28 - o\x00B3noue i\x00F0aaeeueieo cia/oueo aeanyoeiaeo oeeo\x00F0. A \x00B216 - an\x00B3 8 oeeo\x00F0 i\x00F0aaeeuei\x00B3.

2. Iaoiae N\x00B3iiniia.

Aeania cia/aiiy \x00B3ioaa\x00F0aea



iiaeia ciaeoe iaoiaeii N\x00B3iiniia (ia\x00F0aaie). Aeey oeueiai a\x00B3ae\x00F0\x00B3cie [a,b] \x00F0icaeaa\x00BAoueny ia n=2m /anoei ((((((((((h((((((n(A c e\x00F0ieii h=(b-a)/n (1)

O oi/eao O\x00B3 ia/eneththoue cia/aiiy ooieoe\x00B3? O1=f(Xi) \x00B3 ciaoiaeyoue iaaeeaeaia cia/aiiy \x00B3ioaa\x00F0aea ca oi\x00F0ioeith N\x00B3iiniia S = Sn + Rn



Aeae\x00B3 e\x00B3euee\x00B3noue oi/ie \x00F0icaeooy iiaeaith\x00BAoueny \x00B3 cae\x00B3enith\x00BAoueny ioe\x00B3iea oi/iino\x00B3 ia/eneaiue