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

MAPLE 7 VA MATHCAD DASTURIDA KARRALI INTEGRALLARNI HISOBLASH

3-masaladagi integralni hisoblash.
> Int( Int(Int(x+y+2*z,z),y),x)=int(int(int(x+y+2*z,z),y),x);

> Int(Int(Int((x+y+2*z), z = x+y..x+2*y),y = 0..x), x = 1..3)=int(int(int((x+y+2*z), z = x+y..x+2*y),y = 0..x), x = 1..3);

> Int( Int(Int(x+y+2*z,z=x+y..x+2*y),y=0..x),x=1..3)= evalf(int(int(int(x+y+2*z,z=x+y..x+2*y),y=0..x),x=1..3.));

Mathcadda

3-masalaning ishlanish dasturi (Basic tilida)
DEF FNF (X, Y, Z) = X + Y + 2 * Z
DEF FNF1 (X) = 0
DEF FNF2 (X) = X
DEF FNZ1 (X, Y) = X + Y
DEF FNZ2 (X, Y) = X + 2 * Y
DIM X(100), Y(100), Z(100)
DIM Y1(100), Y2(100), Z1(100), Z2(100), U(100), UT(100)
DIM XT(100), YT(100), ZT(100), XTT(100), YTT(100), ZTT(100)
N1 = 0: N2 = 0: N3 = 0: INPUT "N="; N: INPUT "A
'INPUT "C=F1(A),B=F2(B) "; C, D: INPUT "G=Z1(A),H=Z2(B) "; G, H
C = FNF1(A): D = FNF2(B): PRINT "C="; C; " D="; D
G = FNZ1(A, C): H = FNZ2(B, D): PRINT "G="; G; " H="; H
M = FNF(B, D, H): PRINT "M= "; M':INPUT "M= "; M
FOR I = 1 TO N
X(I) = A + (B - A) * RND(1): Y(I) = C + (D - C) * RND(1)
Z(I) = G + (H - G) * RND(1): U(I) = M * RND(1)
Y1(I) = FNF1(X(I)): Y2(I) = FNF2(X(I))
Z1(I) = FNZ1(X(I), Y(I)): Z2(I) = FNZ2(X(I), Y(I)): NEXT I
PRINT " XI YI ZI Y1(I) Y2(I) Z1(I) Z2(I)"
FOR I = 1 TO N
PRINT USING "###.#####"; X(I); Y(I); Z(I); Y1(I); Y2(I); Z1(I); Z2(I): NEXT I
FOR I = 1 TO N
IF Y1(I) <= Y(I) AND Y(I) <= Y2(I) THEN N1 = N1 + 1: XT(N1) = X(I): YT(N1) = Y(I)
NEXT I
PRINT "Y1(I) <= Y(I) <= Y2(I) SHART BO'YICHA Y(I)LAR SONI N1="; N1
FOR I = 1 TO N1
IF Z1(I) <= Z(I) AND Z(I) <= Z2(I) THEN N2 = N2 + 1: XTT(N2) = X(I): YTT(N2) = Y(I): ZT(N2) = Z(I)