Convergence of Improper Integrals of Power Functions

This applet demonstrates the convergence of improper integrals of power functions.
Move the point A to adjust the "proper" bound of the two integrals. When p=1, neither integral converges. When p<1, the left integral exists and the right one does not. When p>1, the right integral exists and the left one does not. (Note that Geogbra does not (yet) support improper integrals. So the depicted areas under the curve are approximations.)