### b) Suppose that a continuous function ( f: mathbb{R}^{2} rightarrow mathbb{R} ) can be written as a product of two continuous functions ( F ) and ( G: mathbb{R} rightarrow mathbb{R} ); namely that ( f(x, y)=F(x) G(y) ) for all ( (x, y) in mathbb{R}^{2} ). In this case, the double integral of ( f ) over the rectangle ( R=[a, b] times[c,

b) Suppose that a continuous function ( f: mathbb{R}^{2} rightarrow mathbb{R} ) can be written as a product of two continuous functions ( F ) and ( G: mathbb{R} rightarrow mathbb{R} ); namely that ( f(x, y)=F(x) G(y) ) for all ( (x, y) in mathbb{R}^{2} ). In this case, the double integral of ( f ) over the rectangle ( R=[a, b] times[c,