% v?nster n=200
n=200;
a=0; b=3;
f=@(x)x.*sin(x);
x=linspace(a,b,n+1);
h=(b-a)/n;
q=sum(h*f(x(1:n)));
result = -1*(q- (sin(3)-3*cos(3)))
%% v?nster n=50
n=50;
a=0; b=3;
f=@(x)x.*sin(x);
x=linspace(a,b,n+1);
h=(b-a)/n;
q2=sum(h*f(x(1:n)));
result2 = -1*(q2- (sin(3)-3*cos(3)))
%% trapets 50a=0;
a=0;
b=3;
n=50;
h=(b-a)/n;
sum=0;
f=@(x) x.*sin(x);
for i=1:1:n-1
    sum= sum + f(a+i*h);

end
result = h/2*(f(a)+f(b)+2*sum)
resultfel = (sin(3)-3*cos(3)) - result

%% trapets 200
a=0;
b=3;
n=200;
h=(b-a)/n;
sum=0;
f=@(x) x.*sin(x);
for i=1:1:n-1
    sum= sum + f(a+i*h);

end
result2 = h/2*(f(a)+f(b)+2*sum)
%% 1b.1
n=50;
a=0; b=1;
f=@(x)x.*cos(x);
x=linspace(a,b,n+1);
h=(b-a)/n;
q2=sum(h*f(x((1:n))))
%% 1b.2
n=50;
fun=@(x,y)x.*cos(x);
h = 1/n;
x = linspace(0,1,n+1);
y = linspace(0,1,n+1);
int=0.0;
for ii=1:n
for jj=1:n
int=int+h^2*fun(x(ii)+h/2,y(jj)+h/2);
end
end
%% 1c
fun = @(x) x.*cos(x);
yess = integral(fun,0,6)