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Laba3_2
Calculation of a definite integral
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Calculation of a definite integral
Analysis of two different ways of subtraction of a certain intgeral. (Condition in the report)
Delphi
program LR3_2;
{$APPTYPE CONSOLE}
uses
SysUtils;
type
TInt = function(x: real): Real;
procedure Method1(Int: TInt; a, b: real);
var S, h, Prev, e: real;
n,i, ie: integer;
begin
S:=Int(a)*(b-a);
e:=0.01;
n:=1;
if abs(S)<e then
begin
write(S:9:4,'|',n:3,'|');
end
else
begin
n:=5;
ie:=2;
while ie<=3 do
begin
repeat
Prev:=S;
S:=0;
h:=(b-a)/n;
for i:=1 to n do
S:=S+h*Int(a+i*h);
n:=n+5;
until abs(S-Prev)<e;
Write(S:9:6,'|',n-5:3,'|');
e:=0.001;
inc(ie);
end;
end;
end;
function Int3(x:real):Real;
begin
result:=1/(Sqrt(Sqr(x)+3.2));
end;
function Int4(x:Real):Real;
begin
Result:=(x+1)*Sin(x);
end;
procedure Method2(a,b:Real;Int:TInt);
var h,Iprev,Icur,E:Real;
n,i,ie:integer;
begin
Icur:=Int(a+h/2)*(b-a);
E:=0.01;
n:=1;
if abs(Icur)<E then
begin
write(Icur:9:4,'|',n:3,'|');
end
else
begin
n:=5;
ie:=2;
while ie<=3 do
begin
repeat
Iprev:=Icur;
Icur:=0;
h:=(b-a)/n;
for i:=0 to n-1 do
begin
Icur:=Icur+Int(a+h/2+i*h);
end;
Icur:=h*Icur;
n:=n+5;
until Abs(Icur-Iprev)< E;
Write(Icur:9:6,'|',n-5:3,'|');
inc(ie);
E:=0.001;
end;
end;
end;
procedure head;
begin
Writeln('|------------------------------------------------------------------|');
writeln('| | 1 method | 2 method |');
Writeln('| |---------------------------|---------------------------|');
writeln('| | e=10^-2 | e=10^-3 | e=10^-2 | e=10^-3 |');
Writeln('| |-------------|-------------|-------------|-------------|');
writeln('| | value | N | value | N | value | N | value | N |');
Writeln('|----------|-------------|-------------|-------------|-------------|');
end;
procedure row(n:integer);
begin
write('|',n,' integral|');
end;
function Int1(x:real):Real;
begin
result:=Sqrt(0.5*x+2)/(Sqrt(2*x*x+1)+0.8);
end;
function Int2(x:real):Real;
begin
result:=Cos(0.8*x+1.2)/(1.5+sin(x*x+0.6));
end;
var k:Integer;
Int:TInt;
begin
head;
k:=1;
while k<=4 do
begin
case k of
1: begin
row(k);
Int:=Int1;
Method1(Int,0.4,1.2);
Method2(0.4,1.2,Int);
Writeln;
Writeln('|----------|-------------|-------------|-------------|-------------|');
end;
2: begin
row(k);
Int:=Int2;
Method1(Int,0.3,0.9);
Method2(0.3,0.9,Int);
writeln;
Writeln('|----------|-------------|-------------|-------------|-------------|');
end;
3: begin
row(k);
Method1(Int,1.2,2.7);
Method2(1.2,2.7,Int);
writeln;
Writeln('|----------|-------------|-------------|-------------|-------------|');
end;
4: begin
row(k);
Int:=Int4;
Method1(Int,1.6,2.4);
Method2(1.6,2.4,Int);
Writeln;
Writeln('|------------------------------------------------------------------|');
end;
end;
k:=k+1;
end;
Readln;
end.