Integrate a spline function squared

I used spline to find an piecewise polynomial for a function. I need to integrate that function squared. How can I do this in Matlab?

Answer 1

[John D'Errico]

Not that hard to do.

x = linspace(0,2*pi,10);
y = cos(x);
spl = spline(x,y);
cnew = zeros(9,7);
for i = 1:9
  cnew(i,:) = conv(spl.coefs(i,:),spl.coefs(i,:));
end
spl.coefs = cnew;
spl.order = 7;
splint = fnint(spl);
diff(fnval(splint,[0,2*pi]))
ans =
      3.147

As a test, how well did we do?

syms u
int(cos(u)^2,[0,2*pi])
ans =
pi

Not too badly at all. I could easily have written the integrals of each segment directly, but as long as FNINT is there, why bother?