# Chapter 21: The Fundamental Theorem of Calculus in One Dimension

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## Introduction

The act of integrating a function and that of differentiating one are inverse operations; thus the area under a curve is an antiderivative of its integrand as a function of the upper end of the area. We explore proof of this claim and its implications for one dimensional integrals.

## Topics

21.1 The Fundamental Theorem for Ordinary Integrals

21.2 The Fundamental Theorem for Integration in on a Path in the Complex Plane

21.3 The Fundamental Theorem in Integration on a Path in Euclidean Space