Deriving Integrals: A Simple Visual Guide

Integration can be understood as the reverse process of differentiation.When we differentiate a function f(x), we get its derivative f'(x).For example, if we have the function f(x) equals x squared.Its derivative is f prime of x equals two x.Differentiation gives us the slope of the curve at each point.Integration, on the other hand, finds the area under the curve.So if the derivative of x squared is two x, then the integral of two x must be x squared plus a constant C.This constant of integration appears because many functions with different vertical shifts share exactly the same derivative.