We propose and analyze two algorithms for multiple integration and L ₁-approximation of functions f:[0,1]^s ® \mathbbRf:[0,1]^s \to \mathbb{R} that have bounded mixed derivatives of order 2. The algorithms are obtained by applying Smolyak's construction (see [8]) to one-dimensional composite midpoint rules (for integration) and to one-dimensional piecewise linear interpolation algorithm (for L ₁-approximation). Denoting by n the number of function evaluations used, the worst case error of the obtained Smolyak's cubature is asymptotically bounded from above by

\frac16p2 s3(s - 1)((s - 2)!)3 ·\frac(log2 n)3(s - 1) n2 ·(1 + o(1))\frac{{16\pi ^2 s}}{{3(s - 1)((s - 2)!)^3 }} \cdot \frac{{(\log _2 n)^{3(s - 1)} }}{{n^2 }} \cdot (1 + o(1))

as n. The error of the corresponding algorithm for L ₁-approximation is bounded by the same expression multiplied by 4 ^s–1.