What is the syntax for the definte integral

Thread starter nameVoid
Start date Mar 13, 2010
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Integral

In summary, a definite integral is a mathematical concept that calculates the area under a curve between two specific points on a graph. It differs from an indefinite integral in that it has specific limits of integration and results in a single numerical value. The standard notation for a definite integral is ∫<sub>a</sub><sup>b</sup> f(x) dx, and it is calculated using integration methods such as Riemann sums, the trapezoidal rule, or Simpson's rule. Some real-life applications include calculating work, revenue, and volume in fields such as physics, economics, and engineering.

Mar 13, 2010

nameVoid

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Mar 13, 2010

Mark44

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Do you mean the LaTeX syntax? If so, rather than explain the syntax, I'll just create the script that renders in a browser as a definite integral. Double-click it and you can see what I did.

[tex]\int_{0}^{\pi} \frac{sin^2(x)}{3} dx[/tex]

If that's not what you're asking, you'll need to be more clear.

1. What is the definition of a definite integral?

A definite integral is a mathematical concept that represents the area under a curve between two specific points on a graph. It is used to find the exact value of an area or the total change in a quantity over a given interval.

2. What is the difference between a definite integral and an indefinite integral?

The main difference between a definite and indefinite integral is that a definite integral has specific limits of integration, while an indefinite integral does not. This means that the result of a definite integral is a single numerical value, while the result of an indefinite integral is a function.

3. What is the syntax for writing a definite integral in mathematical notation?

The standard notation for a definite integral is ∫_a^b f(x) dx, where a and b are the lower and upper limits of integration, and f(x) is the function being integrated. This notation is read as "the integral of f(x) with respect to x, from a to b".

4. How is the definite integral calculated?

The definite integral is calculated using a process called integration, which involves finding the area under a curve by dividing it into small rectangles and summing their areas. This process can be done using various methods such as Riemann sums, the trapezoidal rule, or the Simpson's rule.

5. What are some real-life applications of definite integrals?

Definite integrals have a wide range of applications in different fields, including physics, economics, and engineering. They are used to calculate the work done by a force, find the total revenue or profit in business, and determine the volume of irregularly shaped objects or fluids.