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

1.16143 1.37391 8.24584 0.00000 1.16143 2.53534 3.90926
2.57042 1.13671 3.31732 0.00000 2.57042 3.70713 4.84384
2.26348 1.88293 4.42765 0.00000 2.26348 4.14641 6.02934


Y1(i) <= y(i) <= y2(i) shart bo'yicha y(i)lar soni N1= 13
Z1(i) <= z(i) <= Z2(i) shart bo'yicha z(i)lar soni N2= 1
U(i)
Xtt(i) ytt(i) zt(i) ut(i) FNF(xtt, ytt,zt)
1.21274 2.99824 6.40941 6.94950 17.02980
w= 48
S1= 57.6
Yuqoridagilarga tayangan holda Maple 7 da va Basic tilidan olingan natijalar aniq yechimga qanchalik yaqinligini topamiz:

Aniq yechim y=170/3 va Maple 7 da olingan natija bilan bir xil.

Basic tilidagi natija esa s1=57.6
=(s1-y)/y=(57.6-170/3)/(170/3)=0.016=1,8% demak farq juda katta emas.


4-masala. integralni , integrallash sohasi D: x=1, x=3, y=x², y=x+x² chiziqlar bilan chegaralangan, bo‘lganda hisoblang.
Avvalo aniq hisoblashni ko‘ramiz:



4-masaladagi integralni hisoblash(Maple 7 va Mathcadda).
1. Chegarasiz hisoblash:
> Int( Int((x+y)^2, y),x)=int(int((x+y)^2, y),x);

2. Chegara bo’yicha hisoblash:
> Int( Int((x+y)^2, y=x^2..x+x^2),x=1..3)=
evalf(int(int((x+y)^2, y=x^2..x+x^2),x=1..3));

3.Mathcadda



5-masala. integralni, D: x=0, x=4, y=1, y=5 soha bo‘yicha hisoblang va baholang.
1. Chegarasiz hisoblash.
> Int( Int(x^2+y^2, y),x)=int(int(x^2+y^2, y),x);

2. Chegaraga asosan hisoblash.
> Int(Int(x^2+y^2, x = 0..4), y = 1..5)= evalf(int(int(x^2+y^2, x = 0..4), y = 1..5));

3.Mathcadda olingan natija: