In this paper we present an integral formulation of the active differential photometric stereo algorithm proposed by Clark \cite{clark} and by Iwahori et al \cite{iwahori2,iwahori3}. The algorithm presented in this paper does not require measurement of derivatives of image quantities, but requires instead the computation of integrals of image quantities. Thus the algorithm is more robust to sensor noise and light source position errors than the Clark-Iwahori algorithm. We show that the algorithm presented in the paper can be efficiently implemented in practice with a planar distributed light source, and present experimental results demonstrating the efficacy of the algorithm.