A Darboux integral is a method of calculating the area under a curve, also known as the definite integral. It was developed by French mathematician Gaston Darboux in the late 19th century.
Darboux integral is different from other methods, such as Riemann integration, in that it uses a partition of the interval into subintervals to approximate the area under the curve, rather than the Riemann sum approach.
One advantage of using a Darboux integral is that it allows for a more precise calculation of the area under a curve, as the subintervals can be made smaller and closer together. It also has applications in physics, engineering, and economics.
One limitation of Darboux integral is that it can only be used for continuous functions. It also requires the function to be integrable, meaning it must have a finite area under the curve.
There are many resources available to learn more about Darboux integral, including textbooks, online courses, and tutorials. You can also consult with a math tutor or attend a workshop or seminar on the topic.