The Fundamental Theorem of Calculus

Introduction

The Fundamental Theorem of Calculus forms a bridge between differential and integral calculus. 🐸

The Theorem

Part 1

If f is a continuous real-valued function on a closed interval [a, b], and F is an antiderivative of f in [a, b], then:

∫ba f(x) dx = F(b) - F(a)

Part 2

This part states that the integral of a function over an interval can be computed using one of its antiderivatives.