What would be the correct way to write down the convolution in "star" notation for these two functions; $h(t)$ and $\delta(t-x)$. $\delta$ is the Dirac delta function. The integral notation should be

$$ \int\_{-\infty}^{\infty}h(t-\tau)\delta(\tau-x)d\tau$$

It feels a little awkward with the delta function in there.