Originally Posted by

**jrr** Thanks for your response

Sorry if I am not clear, I am not a mathematician, its an engineering problem which I have tried to describe as best as I can.

1)The experimental data has fundamental limitations which means that it cannot be improved.

2) let me try and explain a little more what I have tried:

Assuming the integrated function is

y=C+a0.x+a1.x^2/2+a2.x^3/3+a3.x^4/4+a4.x^5/5+a5.x^6/6 and the known end points are at x1,y1 and x2,y2

Assume when I evaluate the polynomial at x1 and x2 I get y values of yp1 and yp2, then the errors at the two endpoints are e1 = yp1-y1 and e2 = yp2-y2.

Then I have calculated overall slope error (e2-e1)/(x2-x1) and then subtracted this from a0 in the polynomial

Similarly I have calculated an offset error (e1+e2)/2 and subtracted it from C in the polynomial.

This reduces e1 and e2 but does not make them close enough to zero for my application

So, I am thinking that maybe I need some way of manipulating higher order coeffficints as well?

Hope this helps to clarify the problem