Skip to content
Q61Section ST (Statistics (Q11–Q65))61 of 65

Convergence of a radial singular integral

Let D={(x,y)∈R2:0<x2+y2≤1}D = \{(x, y) \in \mathbb{R}^2 : 0 < x^2 + y^2 \le 1\}. For α≥0\alpha \ge 0, consider the integral Iα=∬D1(x2+y2)α dx dyI_\alpha = \iint_D \frac{1}{(x^2 + y^2)^{\alpha}} \, dx \, dy. Let N0=sup⁡{α≥0:Iα<∞}N_0 = \sup\{\alpha \ge 0 : I_\alpha < \infty\}. Then the value of N0N_0 equals ________ (answer in integer).

Numerical answer: type the number (no options).

Type your answer and check it.