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jostpuur
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What does it mean when an integral sign has a short horizontal line drawn on it?
AiRAVATA said:\fint
But you need to use AMS math package.
A great reference on LaTeX symbols is in the Comprehensive latex symbol list.
The short horizontal line in integral notation is used to represent an infinitesimal change in the variable of integration. It is also known as the differential or dx, and it is a crucial part of the integral that allows for the evaluation of the function over a specific interval.
While the short horizontal line in integral notation may resemble a fraction, it is not a fraction. The dx represents an infinitesimal change in the variable, while the fraction's denominator represents the entire interval of integration. Additionally, the integral sign itself is not an operator in the same way that the division sign in a fraction is.
Yes, it is possible to change the variable of integration in an integral with a short horizontal line. This is known as a variable substitution, and it can be done to simplify the integral or make it easier to evaluate. However, the differential itself (dx) must also be changed accordingly.
If the short horizontal line is missing in integral notation, it means that the function is being integrated with respect to a variable other than x. This is known as a definite integral, where the integral sign without the short horizontal line indicates that the function is being evaluated over a specific interval.
No, the short horizontal line in integral notation is not always necessary. In some cases, the variable of integration and the differential (dx) can be implied based on the context of the problem. However, it is generally good practice to include the short horizontal line for clarity and to avoid confusion.