What is the generalised integral of the square of a function

Thread starter coverband
Start date Jan 28, 2008
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Function Integral Square

In summary, the generalised integral of the square of a function is a mathematical concept denoted by ∫f(x)^2, used to find the area under the curve of a squared function. It is important in solving various mathematical problems and can be calculated using integration techniques. It differs from the generalised integral of a function and can be negative if the function has negative values or when the area under the curve is below the x-axis. However, the value of a definite integral is always positive or zero.

Jan 28, 2008

coverband

For example int[f^2(x)dx]

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Jan 28, 2008

darewinder

i think it depends on the function since u have to use u-sub

but not sure, I am a noob :)

Jan 28, 2008

HallsofIvy

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Homework Helper

First, what do YOU mean by "generalized integral"?

If by that you mean simple the integral of f²(x) for general f, as darewinder said, there is no general formula. It depends strongly on what f is.

1. What is the generalised integral of the square of a function?

The generalised integral of the square of a function is a mathematical concept that involves finding the area under the curve of a function when the function is squared. It is denoted by ∫f(x)^2 and is a type of definite integral.

2. Why is the generalised integral of the square of a function important?

The generalised integral of the square of a function is important because it helps in solving various mathematical problems and is used in many fields such as physics, engineering, and economics. It also helps in understanding the behavior of a function and its properties.

3. How is the generalised integral of the square of a function calculated?

The generalised integral of the square of a function is calculated by using integration techniques such as substitution, integration by parts, or partial fractions. It involves breaking down the function into simpler parts and then integrating each part individually.

4. What is the difference between the generalised integral of a function and the generalised integral of the square of a function?

The generalised integral of a function involves finding the area under the curve of a function, while the generalised integral of the square of a function involves finding the area under the curve of the squared function. The latter is used when dealing with functions that have negative values or when calculating the mean square value of a function.

5. Can the generalised integral of the square of a function be negative?

Yes, the generalised integral of the square of a function can be negative. This occurs when the function has negative values or when the area under the curve of the squared function is below the x-axis. However, the value of a definite integral is always positive or zero.