function y = f( x )
nSamplingPoints = 0.5e4;
if( size(x,1) > 1 && size(x,2) > 1 )
error( 'Matrix-valued evaluation is infeasible.' );
end
% Remark:
% Integrals here could be evaluated far more efficiently in the
% vector-valued case by re-using values that have been calculated
% before. However, this implementation should still be sufficient
% for our needs.
y = zeros(size(x));
for i = 1:length(x)
X = linspace(0,x(i),1+ceil(abs(nSamplingPoints*x(i))));
Y = df(X);
y(i) = trapz(X,Y);
end
end