Editing Constant term (section)

==Constant of integration==
{{main|Constant of integration}}

The [[derivative]] of a constant term is 0, so when a term containing a constant term is differentiated, the constant term vanishes, regardless of its value. Therefore the [[antiderivative]] is only determined up to an unknown constant term, which is called "the constant of integration" and added in symbolic form (usually denoted as <math>C</math>).<ref>{{cite book |author=Arthur Sherburne Hardy |year=1892 |title=Elements of the Differential and Integral Calculus |url=https://books.google.com/books?id=2QgUAAAAYAAJ&dq=%22constant+term%22+%22constant+of+integration%22&pg=PA168 |page=168 |publisher=Ginn & Company}}</ref>

For example, the antiderivative of <math>\cos x</math> is <math>\sin x</math>, since the derivative of <math>\sin x</math> is equal to <math>\cos x</math> based on the [[Differentiation_rules#Derivatives_of_trigonometric_functions|properties of trigonometric derivatives]]. 

However, the ''[[integral]]'' of <math>\cos x</math> is equal to <math>\sin x</math> (the antiderivative), plus an arbitrary constant:

<math display="block"> \int \cos x \, \mathrm dx = \sin x + C,</math>

because for any constant <math>C</math>, the derivative of the right-hand side of the equation is equal to the left-hand side of the equation.