  We use the Euler-Maclaurin formula and the Feynman-Kac formula to extend our
previous method of computation of the spectral action based on the Poisson
summation formula. We show how to compute directly the spectral action for the
general case of Robertson-Walker metrics. We check the terms of the expansion
up to a_6 against the known universal formulas of Gilkey and compute the
expansion up to a_{10} using our direct method.
