# Integration Antiderivative vertical bar [duplicate]

Possible Duplicate:
What is the name of the vertical bar?

When taking a definite integral, the first step is finding the anti-derivative. Once you have gone through all the steps to complete that, you need to evaluate the anti-derivative. This is often written with the formula for the anti-derivative then a vertical bar after that formula with the upper and lower bounds, much like the integration symbol. What is this vertical bar called? Does it have a name? For that matter, does the integration symbol have a name?

This isn't for homework, but neither is it just out of curiosity. I have a reason for wanting to know this, but it would take a while to explain.

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## marked as duplicate by Rahul, 5PM, rschwieb, Micah, Arthur Fischer♦Jan 24 '13 at 4:23

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## 1 Answer

The ∫ symbol $\int$ is used to denote the integral in mathematics. The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz towards the end of the 17th century. The symbol was based on the ſ (long s) character, and was chosen because Leibniz thought of the integral as an infinite sum of infinitesimal summands. See long s for more details on the history of ſ.

The long s survives in elongated form, and with an italic-style curled descender, as the integral symbol ∫ used in calculus; Gottfried Wilhelm von Leibniz based the character on the Latin word summa ("sum"), which he wrote ſumma.

As for the vertical bar denoting the bounds of evaluating an antiderivative:

You might as well call it the "evaluation bar." E.g., it's used here: Evaluation Bar Notation.

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