9.8.5 Surface integrals

(3) Problem: Calculate the surface integral of the 2nd kind: \[ \iint_{S}\left(2 x^{2}+y^{2}+z^{2}\right) d y d z \] where \( S \) is the outer side of the lateral surface of the cone \( \sqrt{y^{2}+z^{2}} \leq x \leq H \).