Program Reshenie_Integrala;
Uses
CRT;
Function f(x:real):real;
Begin
f:=1/sqrt(1+(3*x)+(2*(x*x)));
End;
Var
Int:real;
a,b,i:integer;
x,y,h,e:real;
n:integer;
d1,d2,d3:real;
Function Simpson(n:integer):real ;
Var
rslt:real;
x,h:real;
i: integer;
Begin
h:=abs(b-a)/n;
rslt:=0;
x:=a;
For i:=1 to n Do
Begin
rslt:=rslt+((f(x)+4*f(x+h/2)+f(x+h))*h/6);
x:=x+h;
End;
Simpson:=rslt;
End;
Procedure Sravnenie;
Var
Etalon:real;
Begin
Writeln('‘а ў­Ґ­ЁҐ ®вўҐв®ў');
Write('‚ўҐ¤ЁвҐ § ¤ ­­го в®з­®бвм:');
Readln(e);
Writeln;
n:=1;
While (abs(Simpson(2*n)-Simpson(n))>E) do
n:=2*n;
Etalon:=Simpson(n);
d1:=abs(d1-etalon);
d2:=abs(d2-etalon);
d3:=abs(d3-etalon);
if (d1<d2) And (d1<d3) Then Writeln('ЏҐаўл© ¬Ґв®¤ б ¬л© в®з­л©')
Else if (d2<d3) Then Writeln('‚в®а®© ¬Ґв®¤ б ¬л© в®з­л©') else
Writeln('’аҐвЁ© ¬Ґв®¤ б ¬л© в®з­л©');
Writeln('ђҐ§г«мв в ¬Ґв®¤®¬ ђг­ЈҐ-Љгвв :', etalon:0:4);
End;
Procedure Reshenie;
Begin
Clrscr;
Writeln('„«п аҐиҐ­Ёп Ё­вҐЈа «  (1/sqrt1+3x+2x^2) ўўҐ¤ЁвҐ...');
Write('ЌЁ¦­Ё© ЇаҐ¤Ґ«:');
Readln(a);
Write('‚Ґае­Ё© ЇаҐ¤Ґ«:');
Readln(b);
Write('Ј ўлзЁб«Ґ­Ёп:');
Readln(h);
Writeln ('ЋвўҐвл:
x := a;
Int := 0;
While (x < b) Do
Begin
Int := Int + f(x)*h;
x := x + h;
End;
d1:=Int;
Writeln('”®а¬г«  «Ґўле Їаאַ㣮«м­ЁЄ®ў: ', Int:0:4);
x := a + h; Int := 0;
While (x < b) Do
Begin
Int := Int + 1/2*h*(f(x - h) + f(x));
x := x + h;
End;
d2:=Int;
Writeln('”®а¬г«  ва ЇҐжЁ©: ', Int:0:4);
x := a ; Int := 0;
While (x < b) do
Begin
Int := Int + h*(f(x) + 4*f(x + h/2) + f(x + h))/6;
x := x + h;
End;
d3:=Int;
Writeln('* ЊҐв®¤ ‘Ё¬Їб®­ : ', Int:0:4);
Sravnenie;
Readkey;
End;
Begin
Clrscr;
Repeat
WriteLn('Џа®Ја ¬¬  ¤«п аҐиҐ­Ёп Ё­вҐЈа « , 3 бЇ®б®Ў ¬Ё.');
WriteLn('ЊҐв®¤®¬ "ваҐгЈ®«м­ЁЄ®ў", ва ЇҐжЁ©, ‘Ё¬Їб®­ .');
Writeln('ЊҐ­о Їа®Ја ¬¬л:');
Writeln('ђҐиҐ­ЁҐ Ё­вҐЈа «  - "1"');
Writeln('‚л室 - "2"');
readln (n);
Case n of
1: Reshenie;
2: halt;
End;
Until n<>0;
End.