Question

If f is a constant function, f(x y) = k, and R = [a, b] x [c, d], show that double int k dA = k(b - a)(d - c)

Answer 1

So when you integrate over this region, you can bust it up into integrals with respect to dy and dx with those limits of integration. Iterated integrals they call them.
\[\iint_{R}k\;dA=\int\limits_{a}^{b}\int\limits_{c}^{d}k\;dydx=\int\limits_{a}^{b}\left [\int\limits_{c}^{d}k\;dy \right ]dx\]