Action-angle transformation

In classical mechanics, usually in Lagragian and Hamilton formalisms, one needs to deal with a special kind of transformation called "Canonical Transformation" and inside this, there is still a very specific type of change of variable called "Action-angle variable" which makes it clear whether or not our system is integrable. One example of integration involved in the transformation is as follow,

$\displaystyle \int_{r_{min}}^{r_{max}} \sqrt{(1-\dfrac{r_{min}}{r})(\dfrac{r_{max}}{r}-1)} dr$

Find the value of this integral when $r_{min}=1$ and $r_{max}=10$ .

Bonus:Try to evaluate this integral for arbitrary upper and lower limits.