DefinitionMeaning: The Fundamental Theorem of Calculus define the link between finding the slope at a point on a curve and finding the area under a curve (and consequently also give a nice way to compute definite integrals. The first part draws a connection between the definite integral of a function and antiderivatives and the second part describes the function that gives us the value of the derivative of the integral of a function. The fundamental theorem of calculus underlies integral calculus, providing the relationship between the two branches of calculus, differential and integral, and giving a method to compute the area, volume or quantities which may be extensible and cumulative. This is used in physics, engineering, and a wide range of other applications including managerial and quantitative economics for solving problems involving 'very fast rates or very small changes in quantities' and also to assist in long term predictions of a wide range of variables which are constantly changing. For example, if f(x) is a continuous function on the interval [a,b], then ∫abf(x)dx is equal to to difference of the antiderivative F(x) of f(x) at b and a, i.e., ∫abf(x)dx=F(b)−F(a).
