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1. . , , .
2. , :
;
;
;
.
9.1.
, .
:
LAB :
>> f=inline('reallog(x)'); %
>> a=3;
>> b=5;
>> N=100;
>> i=1:N;
>> dx=(b-a)/(N-1); %
>> x=a:dx:b; %
>> y=feval(f,x); %
%
>> m=2:N;
>> y1(m-1)=y(m);
>> Fr=sum(y1)*dx
Fr =
2.7565
%
>> m=1:N-1;
>> y1(m)=y(m);
>> Fl=sum(y1)*dx
Fl =
2.7462
%
>> s=0;
>> for i=2:N-1
s=s+y(i);
end;
>> Ft=(0.5*y(1)+s+0.5*y(N))*dx
Ft =
2.7513
%
>> s=0;
>> for i=2:N-1
if i-2*ceil(i/2)==0
k=4;
else
k=2;
end;
s=s+k*y(i);
end;
>> Fs=(y(1)+s+y(N))*dx/3
Fs =
2.7405
9.2.
-.
:
:
, (9.1)
n , , N , S ;
:
, (9.2)
xi [ a, b ].
LAB :
>> f=inline('reallog(x)');
>> a=3; %
>> b=5;
>> Ymin=0;
>> Ymax=feval(f,b);
>> N=1000; %
>> x=a+(b-a)*rand(N,1);
>> y=Ymin+(Ymax-Ymin)*rand(N,1);
>> s=0; % ,
>> for i=1:N
if y(i)<=feval(f,x(i))
s=s+1;
end;
end;
>> Fmk=s*(b-a)*(Ymax-Ymin)/N %
Fmk =
2.7425
% (9.2)
>> F=feval(f,x);
>> Fmk=(b-a)*sum(F)/N
Fmk =
2.7463
MATLAB :
ü quad(¢fun¢, a, b, tol) fun [a, b] tol ( tol=10-3), ;
|
|
ü int(y(x), a, b) y(x) [a, b] ( , ).
9.3.
.
quad :
>> y='log(x)';
>> quad(y,3,5)
<Enter> :
ans =
2.7514
int:
>> syms x; %
>> y=log(x); %
>> int(y,3,5)
ans =
5*log(5)-2-3*log(3)
f (x) [ a, b ] , , , - 2000
.
f (x) | [ a, b ] | f (x) | [ a, b ] | ||
[0; 3] | [1,5;2,5] | ||||
[0; 1] | [1; 7] | ||||
[1; 2] | [0; 1] | ||||
[2; 3] | [0; 3] | ||||
[2; 3] | [0; ] | ||||
[1; 2] | [0; 5] |
.
f (x) | [ a, b ] | f (x) | [ a, b ] | ||
[0; 3] | [1,5;2,5] | ||||
[0; 1] | [1; 7] | ||||
[1; 2] | [0; 1] | ||||
[2; 3] | [0; 3] | ||||
[2; 3] | [0; ] | ||||
[1; 2] | [0; 5] |
- MATLAB.
- MATLAB.
- .
- MATLAB
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