We propose an informative path planning (IPP) algorithm for active classification using an unmanned aerial vehicle (UAV), focusing on weed detection in precision agriculture. We model the presence of weeds on farmland using an occupancy grid and generate plans according to information-theoretic objectives, enabling the UAV to gather data efficiently. We use a combination of global viewpoint selection and evolutionary optimization to refine the UAV's trajectory in continuous space while satisfying dynamic constraints. We validate our approach in simulation by comparing against standard "lawnmower" coverage, and study the effects of varying objectives and optimization strategies. We plan to evaluate our algorithm on a real platform in the immediate future.