We derive a formula for the trace of a class of differential operators defined by forced two point boundary value problems. The formula involves finite-dimensional computations with matrices whose dimension is no larger than the order of the differential operator. Thus, we achieve an exact reduction of an infinite-dimensional problem to a finite-dimensional one. We relate this trace calculation to computation of the H-2 norm for certain infinite-dimensional systems. An example from fluid dynamics is included to illustrate the method.