Henstock-Kurzweil integral

The Henstock-Kurzweil integral is a method of defining the area under a curve that extends traditional techniques like the Riemann integral. It allows for integrating more complex, irregular functions by considering variable-sized intervals that adapt to the function's behavior. This flexibility enables it to handle functions with highly oscillatory or discontinuous parts, providing a more powerful and versatile approach to integration. Essentially, it offers a precise way to measure total accumulation even in difficult cases where standard methods may fail, making it valuable in advanced mathematical analysis and applications.