👉 Integral calculus is a branch of mathematics that deals with the study of continuous change, particularly focusing on finding areas under curves, volumes of solids, and accumulation of quantities. It is fundamentally based on the concept of summing up infinitesimally small pieces (infinitesimals) to approximate a total. The definite integral, denoted as ∫[a, b] f(x) dx, calculates the net area between a function f(x) and the x-axis over the interval [a, b]. The process involves dividing the interval into smaller subintervals, approximating the area of each subinterval using rectangles, and summing these approximations. As the number of subintervals increases, this sum approaches the exact area under the curve, providing a precise value. This approach is encapsulated in the Fundamental Theorem of Calculus, which links differentiation and integration, showing that finding the derivative of an integral returns the original function, thus establishing a powerful connection between these two core concepts in calculus.
