The symmetry energy of a nucleus is determined in a local density approximation and integrating over the entire density distribution of the nucleus, calculated utilizing the relativistic density-dependent Thomas-Fermiapproach. The symmetry energy is found to decrease with increasing neutron excess in the nucleus. The isovector coupling channel reduces the symmetry energy, and this effect increases with increased neutron excess. The isovector coupling channel increases the symmetry energy integral in $^{40}$Ca and reduces it in $^{48}$Ca, and the interplay between the isovector and the isoscalar channels of the nuclear force explains this isotope effect.