In this paper, we introduce the concept of total integrals in the case of weak Hopf algebras, which is a generalization of the total integral introduced by Menini and Militaru. We give two necessary and sufficient conditions for the existence of a total integral, and study when the category M_A ~(coH) of right modules and the category ~HM_A of weak Doi-Hopf modules are equivalent under the assumption that there exists a total integral, where A ~(coH) denotes the coinvariant subalgebra of the weak left H-comodule algebra A. In the end, we give some applications of the affineness criterion for weak Doi-Hopf modules.
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