This article explores the conceptual challenges that engineering students encounter with double integrals in a vector calculus course. Drawing on previous literature and utilising APOS (Activity- Process- Objects- Schema) as a theoretical framework, this study investigates the difficulties that students face in understanding and applying double integrals. By analysing responses to a written test that assesses students' conceptual understanding of double integrals and student responses in interviews, this research sheds light on specific areas where students struggle, such as curve sketching, identifying regions of integration and changing the order of integration. Swapping the order of integration in double integrals is the focus of this research study. The findings of this study have the potential to contribute to the enhancement of teaching and learning strategies for double integrals to better support engineering students' conceptual comprehension and proficiency in this important mathematical concept.