  We employ a thermodynamic integration method (TIM) to establish the values of
the residual entropy for the geometrically frustrated spin-s triangular Ising
antiferromagnet, with the spin values s = 1/2, 1, 3/2, 2 and 5/2. The case of s
= 1/2, for which the exact value is known, is used to assess the TIM
performance. We also obtain an analytical formula for the lower bound in a
general spin-s model and conjecture that it should reasonably approximate the
true residual entropy for sufficiently large $s$. Implications of the present
results in relation to reliability of the TIM as an indirect method for
calculating global thermodynamic quantities, such as the free energy and the
entropy, in similar systems involving frustration and/or higher spin values by
standard Monte Carlo sampling are briefly discussed.
