# Stokes' theorem

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In differential geometry, Stokes' theorem (or Stokes's theorem, also called the generalized Stokes' theorem) is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus. William Thomson first discovered the result and communicated it to George Stokes in July 1850.[1][2] Stokes set the theorem as a question on the 1854 Smith's Prize exam, which led to the result bearing his name.[2]

## Contents

### Introduction

The fundamental theorem of calculus states that the integral of a function f over the interval [a, b] can be calculated by finding an antiderivative F of f:

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