I am a naval engineering student and have a problem with Simpson rules. I am using rule for calculation of a surface of waterline (that is a surface of a ship at particular draft and it looks like a polynomial curve and surface under which can be calculated by using Simpson rules). How can i calculate a surface under curve if the y coordinates for every x are given? What about if I have given $X/2$ and $y/2$? Can I use both Simpson 1 rule (coefficients $1,4,2,4,..1$) and Simpson 2 rule $(1,3,3,2,3,3,..1)$ at the same time? What coefficients shall I use if I have given 17 x and of which ones between $0$ and $1$ and $17$ and $18$ are divided to quarters? $(-0.75,-0.5,-0.25,0,1,2,3,...17,17.25,17.5,17.75)$
Thank you!