MATLAB: To find area of parabola

matrix

parabola going from three point (7.8 0.96), (8.25 0.99), (8.55 0.94), how can I compute area under the parabola?
x=[7.8 8.25 8.55];
y=[0.96 0.99 0.94];
p=polyfit(x,y,2);
f=polyval(x,p);
plot('x','y','o','x','f','-');

Best Answer

x=[7.8 8.25 8.55];
y=[0.96 0.99 0.94];
p=polyfit(x,y,2);
%f=polyval(x,p);                x & p should be reversed
%plot('x','y','o','x','f','-');  read plot documentation
% method 1
t = linspace(x(1),x(3));
yhat = polyval(p,t);
a1 = trapz(t,yhat);
% method 2
f = @(v) p(1)*v.^2+p(2)*v+p(3);
a2 = quadgk(f,x(1),x(3));
a1,a2
a1 =
      0.7344
a2 =
      0.7344
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