The integral of 1/r over the unit disk U is given by integral integral_U (d A)/r | = | integral integral_U (d x d y)/sqrt(x^2 + y^2) | = | integral_0^(2π) integral_0^1 (r d r d θ)/r | = | 2π integral_0^1 d r | = | 2π. In general, integral integral_U r^n d A = 2π integral_0^1 r^(n + 1) d r = (2π)/(2 + n) provided n>-2.

double integral | unit disk | unit square integral