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It has long been known that the multivariate integration problem for the unitball in $C^r([0,1]^d)$ is intractable for fixed finite $r$. H. Wo\'zniakowskihas recently conjectured that this is true even if $r=\infty$. This paperestablishes a partial result in this direction. We prove that the multivariateintegration problem, for infinitely differential functions all of whosevariables are bounded by one, is not strongly tractable.

Multivariate integration in C^\infty([0,1]^d) is not strongly tractable