Answer to Question #190577 in Calculus for Mel

Question

Explain Fundamental Theorem of Calculus (Integrate a variety of functions)

Answer 1

The fundamental theorem of calculus states that it links the concept of differentiating a function with the concept of integrating a function.

It states that one of the antiderivatives (also known as an indefinite integral), say F, of some function f may be obtained as the integral of f with a variable bound of integration.

It implies the existence of antiderivatives for continuous functions.

The theorem also states that the line integral of the gradient of the function f , gives the total change in the value of the function f from the start ti the end of curve.