(Last Updated On: December 13, 2017)
The theorem that establishes the connection between the two branches of calculus: differential calculus and integral calculus. The fundamental theorem of calculus is typically given in two parts. It says the following:
Suppose f is continuous on [a, b]. Then:
(1) The function
is an antiderivative of f,
i.e., g'(x) = f(x).
(2) (Evaluation Theorem) If F is an antiderivative of f, i.e. F'(x) = f(x), then
The two parts of the theorem can be rewritten like this:
Important: The theorem states that integration and differentiation are inverse operation. For the derivative of an integral of a function yields the original function, and the integral of a derivative also yields the function originally differentiated (up to a constant).
credit: James Stewart©2013 www.PinoyBIX.com