The Area Problem and the Definite Integral Integration is vital to many scientific areas. Many powerful mathematical tools are based on integration. Differential equations for instance are the direct consequence of the development of integration.
Integration stems from two different problems.
The more immediate problem is to find the inverse transform of the derivative. This concept is known as finding the antiderivative . The other problem deals with areas and how to find them. The bridge between these two different problems is the Fundamental Theorem of Calculus. We want to find the area of a given region in the plane.