Double integral of ln(1+x^2+y^2) over the region x^2+y^2 ≤ e^2-1

Published on December 25, 2024

The double integral, using polar coordinates and integration by parts, evaluates to π(e^2 + 1).

Question

∫∫ D ln(1+x^2 +y^2 )dxdy D = x^2 + y^2 ≤ e^2 - 1