One of the main challenges in volume rendering algorithms is how to compute the Volume Rendering Integral accurately, while maintaining good performance. Commonly, numerical methods use equidistant samples to approximate the integral and do not include any error estimation strategy to control accuracy. As a solution, adaptive numerical methods can be used, because they can adapt the step size of the integration according to an estimated numerical error. On CPU, adaptive integration algorithms are usually implemented recursively. On GPU, however, it is desirable to eliminate recursive algorithms. In this work, an adaptive and iterative integration strategy is presented to evaluate the volume rendering integral for regular volumes, maintaining the control of the step size for both internal and external integrals. A set of computational experiments were made comparing both accuracy and efficiency against the Riemann summation with uniform step size. The proposed algorithm generates accurate results, with competitive performance. The comparisons were made using both CPU and GPU implementations.