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An investigation was conducted to estimate the error when a flat-flux approximation is used to compute the resonance integral for a simple absorber element embedded in a neutron source. An integral equation describing the collision rate as a function of energy, position, and angle is constructed and subsequently specialized to the case of energy and spatial dependence. This equation is further simplified by expanding the spatial dependence in a series of Legendre polynomials. In this form, the effects of slowing down and flux depression may be accounted for to any degree of accuracy desired. The resulting integral equation for the energy dependence is thus solved numerically, considering the slowing down and the infinite-mass model as separate cases. From the solution obtained by the above method, the error ascribable to the flat-flux approximation is obtained. In addition to this, the error introduced in the resonance integral in assuming no slowing down in the absorber is deduced.