1. The problem statement, all variables and given/known data An infinite plane slab of thickness 2d lies in the xy-plane with −d<z<d. Its charge density is given as ρ = kz2 for −d<z< d and zero otherwise. (i) Find the electric field, E(z), for all z. 2. Relevant equations Gauss' law 3. The attempt at a solution This problem is pretty easy to do with a gaussian surface. However. I wanted to know if I could also do it by calculating the field directly from coulombs law (I know it would be far more tedious but I'm just curious) with the integral 1/4∏ε0∫Vρ/r2dv = 1/4∏ε0∫∫∫ρ/(x2+y2+z2) dxdydx where the integrals of y and x run from -∞ to ∞ and the integral of z runs from -d to d. But if so, this integral would only hold for being outside the slab right?