# Question on Integrating Over Joint Probability

Let us say that we have a joint probability density denoted as $$P(x_1,x_2,...,x_n)$$

If we are trying to find the probability that every $x_i$ is greater than $0$, is it correct to say that the probability of that will be:

$$\int_{0}^{\infty}\int_{0}^{\infty}...\int_{0}^{\infty}P(x_1,x_2,...,x_n)dx_1dx_2...dx_n$$

Assuming $x_i$ belongs to a continuous distribution with an infinite range.

If this is incorrect, what is the correct expression.