In bayes version for continuous case, what does it mean to integrate with respect to $d\theta$ when $\theta$ is a vector not a a scalar value?

$$p(\theta|D) = \frac{p(D|\theta)p(\theta)}{p(D)}$$

Where $D$ is a set of observed data points, and $\theta$ is a vector of parameters to be estimated.

$$ p(D) = \int p(D|\theta)p(\theta)d\theta $$

Is this integral a surface integral, component-wise integral or what ?