FTC 2 relates a definite integral of a function to the net change in its antiderivative. Fundamental Theorem of Calculus (Part 2): If f is continuous on [ a, b], and F ′ (x) = f (x), then ∫ a b f (x) d x = F (b) − F (a). This FTC 2 can be written in a way that clearly shows the derivative and antiderivative relationship, asWhat is the significance of the Part 2 theorem?
The part 2 theorem is quite helpful in identifying the derivative of a curve and even assesses it at definite values of the variable when developing an anti-derivative explicitly which might not be easy otherwise. The theorem bears ‘f’ as a continuous function on an open interval I and ‘a’ any point in I, and states that if “F” is demonstrated byWhich part of the fundamental theorem creates a link between differentiation?
Part 1 of Fundamental theorem creates a link between differentiation and integration. By that, the first fundamental theorem of calculus depicts that, if “f” is continuous on the closed interval [a,b] and F is the unknown integral of “f” on [a,b], thenWhat is the difference between the fundamental theorem and the corollary?
The fundamental theorem is usually applied to calculate the definite integral of the function f for which an antiderivative F is known. Especially, if f is a real-valued continuous function on [a, b] and F is an antiderivative of f in [a, b], then The corollary allows continuity on the complete interval.