Improper integrals outside domains

Question

What is the standard convention for computing something like

$$\int_0^3 \frac{1}{\sqrt{1-x}}\,\mathrm{d}x? $$

Is it equivalent, since the integrand is not defined on $(1,\infty)$, to $$\int_0^1 \frac{1}{\sqrt{1-x}} \, \mathrm{d}x$$ where one can use the standard technique for an improper integral, or does it simply not exist?

Answer 1

For $x>1$, the term $ \frac{1}{\sqrt{1-x}}$ is not defined. Hence $\int_0^3 \frac{1}{\sqrt{1-x}}\,\mathrm{d}x$ is nonsense.