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Asked by S on 14 May 2013

For computation of area the value of y1,y2 and y3 are coming from three different same dimension matrix and so I want to compute area of using this code for same matrix dimension as y1, y2 and y3?

x=[7.8 8.25 8.55]; y=[0.96 0.99 0.94]; p=polyfit(x,y,2); t=linspace(x(1),x(3)); yhat=polyval(p,t); a1=trapz(t,yhat);

How can I improve code for all 3*3 matrix of given y1,y2 and y3, result will be area a1 of 3*3 matrix.

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Answer by Roger Stafford on 14 May 2013

This general formula in terms of x1, x2, x3, y1, y2, and y3 gives the exact area under your 'polyfit' curve without the trapezoidal approximation errors introduced by 'trapz'. That is, it is the exact integral from x = x1 to x = x3 of the unique quadratic function which passes through all three points (x1,y1), (x2,y2), and (x3,y3).

a = (x3-x1)*((y1+y2+y3)/3+((x3-x2)*(y2-y1)/(x2-x1)-(x2-x1)*(y3-y2)/(x3-x2))/6);

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S on 16 May 2013

and I also want to know how can I read y1, y2 and y3 from three different files keeping x1,x2 and x3 as

x=[7.8 8.25 8.55];

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