Question : Find the electric field at the centre of a ball of radius R with volume charge density rho = a.r, where a is a constant vector and r is a radius vector drawn from ball's centre. Relevant Equations and attempt at solution : I used the basic formula for electric field due to continuous volume charge density and arrived at an equation which I tried to solve two different ways as shown in image. I am getting different solutions by trying different methods which is not possible. I have tried to think of a reason for this and my reasoning for this anomaly has been shown in the image. Please help me in figuring out where my approach went wrong.