Mundarija kirish aniq integrallarni taqribiy hisoblash. Eng sodda interpolyatsion kvadratur formula to‘G’ri to‘rtburchaklar formulasi trapetsiyalar formulasi

1.52804 9.63106 5.69143 4.58413 12.22434 3.34052
3.91932 12.84398 1.66968 11.75795 31.35454 4.09430
0.64177 5.21029 3.87952 1.92530 5.13413 2.41910
N1= 10
Y=1
2.82219 17.06957 3.47711 4.46002
3.45048 25.29536 2.24122 5.36151
3.84781 27.88627 0.33742 5.63330
3.79823 11.64860 3.14921 3.93024
1.87480 9.54129 3.73618 3.37877
2.59128 8.44137 1.67605 3.32154
3.31921 26.38727 3.53498 5.45036
3.94437 29.15086 1.36120 5.75285
1.52804 9.63106 5.69143 3.34052
3.91932 12.84398 1.66968 4.09430


N2= 8
xtT(i) ytT(i) ztT(i) FNF(xtT(I), ytT(I))
2.82219 17.06957 3.47711 4.46002
3.45048 25.29536 2.24122 5.36151
3.84781 27.88627 0.33742 5.63330
3.79823 11.64860 3.14921 3.93024
1.87480 9.54129 3.73618 3.37877
2.59128 8.44137 1.67605 3.32154
3.31921 26.38727 3.53498 5.45036
3.94437 29.15086 1.36120 5.75285
w= 128
S1= 307.2
Yuqoridan ko`rinib turibdiki aniq yechim y=162.1 va biz Basic tilida hisoblab topgan yechimimiz s1=307.2. endi xatolikni baholab olamiz:
=(s1-y)/y=(307.2-162.1)/162.1=0.90=90% Demak, xatolik 90% , bundan ko`rinib turibdiki, biz random orqali tanlab olgan ixtiyoriy x, y o`zgaruvchilarimiz hisoblashda juda katta xatolikni keltirib chiqarar ekan, dasturdan olingan natija hisob-kitobimizni umuman qanoatlantirmaydi desak mubolag`a bo`lmaydi. Shu sababli ham o`zgaruvchilarni tanlashda alohida e`tibor qaratish lozim.


3-masala. V = {1x3, 0yx, x+yzx+2y integrallash sohasi asosida

integralni (2.41) formula asosida hisoblang.
(2.41) formula dagi o‘zgaruvchilarni berilgan misoldagi qiymatlari a=1, b=3, s=0, d=3, y=1, h=9

Bu holda quyidagicha almashtirish qilamiz:
x=1+2, u=3, z=1+8, n=24
Tasodifiy sonlar jadvaldan 80 ta qiymat olamiz (N=20). Jadvaldan y_i (i = 1, 2, .. 20) shartni qanoatlantiruvchi u_i larni topamiz, ular 11 ta, bularga mos keluvchi larni aniqlaymiz ular 3 ga teng, bu 3 ta songa mos keluvchi y_i ni y_iU_i shartga asosan topamiz u n=1.
Demak,
Berilgan integral aniq yechimi:

Xatolikni baholaymiz: