program lab4_11v;
uses Crt;
const a = 0;
      b = 3;
      E = 0.001;


 function arcsin(x:real):real;
 begin
  if x=1.0 then arcsin:=Pi/2.0
  else arcsin:=arctan(x/sqrt(1-x*x));
 end;

 function fpp(x:double):double;
 begin
  fpp:= x;
 end;

 function f(x:double):double;
 begin
  f:=arcsin(sqrt(x/(1+x)));
 end;

 var
  sum, h,n,M,x,Xnext,I : double;

begin
 ClrScr;
 sum:=0;

 M := 2.12132;{max|f''(x)|}

 h := sqrt( (24*E) / ((b-a)*M) );
 n := ((b-a)/h);
 writeln('h = ',h);
 writeln('n = ',n);

 n := sqrt( ((b-a)*(b-a)*(b-a)*M)/(24*E) );
 writeln('n = ',n);

 x:=a;
 repeat
 begin
  Xnext := x+h;
  sum := sum + f((x+Xnext)/2);
  x := Xnext;
 end;
 until  (Xnext<=(b-h));

 I:= sum*h;
 writeln('I = ',I);

 readln;
end.