Complex 3d+ distance formula solve maybe

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[tex]f(x,y)=\sqrt{\sum_{i=0}^{dimensions}(O_i+X_i x+Y_i y-P_i)^2}[/tex] next solve [tex]\int f(x,y) dx[/tex] next convert to t values like [tex]x=(x_{j}+t(x_{j+1}-x_{j}))[/tex] and [tex]y=(y_{j}+t(y_{j+1}-y_{j}))[/tex] on a per line basis with over vertices number is 0th and substitute into [tex]\sum_{j=0}^{vertices}\int_{0}^{1} result(x_t,y_t) dt[/tex] and finally we have a result, how do I go from start to solution? If it helps, I am doing this on planar so like 2d, closed, not self intersecting, not all equal or collinear, and straight line polygons in 3d+ (3d, 4d, and above) space and using Green's Theorem to do it and I am certain that this form is correct, can you contact maybejosiah@aol.com if you have a solution? I hear there is possibly a way to convert to sine and cosine values with this for values, what are my options assuming that f(x,y)>=0 and points can be anywhere? Note that O is origin of 2d plane so like 0,0 on plane but anywhere in 3d+, X is what x vector is in 3d+, similar to X for Y for y values, and P is other point to compare with, any takers to inform me how to do this?