#Funktion
function retval = g(x);
retval = arrayfun(@(x) exp(x) * x.^2, x);
endfunction

#Parameter
k = 1
t = 0
N = 2.^k #Intervall-Anzahl
r = k ./ 10
a = 0
b = r
h = (b - a) ./ N;
x = a:h/2:b
y = g(x)

function retval = Quadrature0(y, a, b, N, h)
retval = 0;
for ii = 1:N
retval = retval + y(2 .* ii);
end
retval = retval .* h;
endfunction

function retval = Quadrature1(y, a, b, N, h)
retval = y(1) + y(2 .* N +1);
for ii = 1:N
retval = retval + 2 .* y(2 .* ii -1);
end
retval = retval .* (h ./ 2);
endfunction

function retval = Quadrature2(y, a, b, N, h)
retval = y(1) + y(2 .* N +1);
for ii = 1:N
retval = retval + 2 .* y(2 .* ii -1) + 4 .* y(2 .* ii);
end
retval = retval .* (h ./ 6);
endfunction

Quadrature0(y, a, b, N, h)
Quadrature1(y, a, b, N, h)
Quadrature2(y, a, b, N, h)

#Konstanten
enull = 8.859E-12
sig = 0.36
konst = exp(((-sig).* t)./(enull)) .* (enull .* r.^2)^(-1)

Ergebnis0 = konst .* Quadrature0(y, a, b, N, h)
Ergebnis1 = konst .* Quadrature1(y, a, b, N, h)
Ergebnis2 = konst .* Quadrature2(y, a, b, N, h)