i.1.51 Double integrals
Condition: Calculate the moment of inertia about the axis \( O Z \) of a homogeneous section of the surface \( z=\sqrt{x^{2}+y^{2}},(0 \leq z \leq 1) \).
Double and iterated integrals over various areas of integration, conversion from Cartesian to polar coordinates, calculation of the Jacobian, changing the limits of integration, transformation of variables in the integral.