Question

The surface charge density of an object is σ = dq/dA.

Why is the total charge on the surface,

Q = double integral σ dA ?

Answer 1

total charge on surface = surface charge density* area
basically, surface charge density is the charge per unit area ...which means how much charge does an unit area has. so here \[q=\int\limits_{0}^{A}dA*\sigma \]

Answer 2

if charge density would have varied then we might have used
\[q= \int\limits_{0}^{A}dA* \sigma + \int\limits_{0}^{\sigma} d \sigma*A\]