= Integral first-order Taylor formula for a vector map
{title2=$F(x+h)-F(x)=\int_0^1DF(x+th)h\,dt$}
For a continuously differentiable <vector-valued function> whose domain contains the segment from $x$ to $x+h$, apply the <fundamental theorem of calculus> componentwise to $t\mapsto F(x+th)$. The resulting integral matrix is valid even when there is no common intermediate point giving a vector mean-value formula. For a <score function>, it integrates the <Hessian matrix> along the segment to a candidate estimate.
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