If f(x) and g(x) are continuous functions satisfying f(x) = f(a – x) and g(x) + g(a – x) = 2, then what is \(\mathop \smallint \nolimits_0^{\rm{a}} {\rm{f}}\left( {\rm{x}} \right){\rm{g}}\left( {\rm{x}} \right){\rm{dx}}\) equal to?
1
\(\mathop \smallint \nolimits_0^{\rm{a}} {\rm{g}}\left( {\rm{x}} \right){\rm{dx}}\)
2
\(\mathop \smallint \nolimits_0^{\rm{a}} {\rm{f}}\left( {\rm{x}} \right){\rm{dx}}\)
3
\(2\mathop \smallint \nolimits_0^{\rm{a}} {\rm{f}}\left( {\rm{x}} \right){\rm{dx}}\)
4
0