Gaussian Integration: Int(0,1000)g(x)[f(x)]dx

[eljose79]

I have some doubts about it..in fact when you want to calculate an integral numerically..i always use gaussian integration but what would happen if i use this technique to calculate:

Int(0,1000)g(x)[f(x)]dx where [] means the floor function in fact it is a non-continuous function..would be gaussian integration valid in this case?...

 

[mathman]

It would still be valid, but you'd be better off doing the integral separately for each interval between the jumps.

 

[tacman]

Gaussian integration is a numerical method used to approximate integrals by breaking them down into smaller intervals and using a weighted sum of function values at specific points within each interval. This method is typically used for continuous functions, as the weights and points are chosen based on the function's smoothness.

In the case of a non-continuous function, such as one with a floor function, Gaussian integration may not be the most accurate method. This is because the points and weights are chosen based on the function's smoothness, and a non-continuous function may not have a well-defined smoothness.

However, it is still possible to use Gaussian integration for non-continuous functions by modifying the weights and points to better fit the function's behavior. This may require some trial and error, as there is no set formula for choosing the weights and points in this case.

Alternatively, there are other numerical integration methods that may be better suited for non-continuous functions, such as the trapezoidal rule or Simpson's rule. These methods may be more accurate and efficient for calculating integrals involving non-continuous functions.

In summary, while Gaussian integration is a commonly used method for numerical integration, it may not be the best choice for non-continuous functions. It is important to consider the behavior of the function and choose an appropriate integration method for accurate results.