For a function f(x, y, z) with domain R such that a ≤ x ≤ b, c ≤ y ≤ d, k ≤ z ≤ l,
∫ab∫cd∫klf(x, y, z)dzdydx =
∫ab∫kl∫cdf(x, y, z)dydzdx =
∫cd∫ab∫klf(x, y, z)dzdxdy =
∫cd∫kl∫abf(x, y, z)dxdzdy =
∫kl∫ab∫cdf(x, y, z)dydxdz =
∫kl∫cd∫abf(x, y, z)dxdydz =
∫∫∫Rf(x, y, z)dV