# Integral of inner product of $\langle x, A(t) \dot{x}\rangle$

Let $$A(t)$$ be uniformly positive definite for any $$t$$, and $$x(t)$$ is a vector, and $$x(0)$$ is a finite.

since $$\int_0^t x(\tau)\dot{x}(\tau)\,\mathrm d\tau = \frac{1}{2}[x(t)^2-x(0)^2]$$ is finite, I wonder whether $$\int_0^t x(\tau) A(\tau) \dot{x}(\tau)\,\mathrm d\tau > -\infty$$ ?

Thanks