- #1
ergonomics
- 14
- 0
if a function f is not integrable does it imply, that there exists such an epsilon that whichever partition P i choose it will follow this condition
Uf,p-Lf,p>=Epsilon?
Uf,p-Lf,p>=Epsilon?
Last edited:
The Upper Darboux Integral is a method of calculating the area under a curve using rectangles. It is a type of Riemann Integral that uses the upper bound of the function to determine the height of the rectangles.
The Upper Darboux Integral is different from other types of integrals, such as the Riemann Integral and the Lebesgue Integral, because it uses the upper bound of the function to determine the height of the rectangles instead of the lower bound or a combination of both.
The Upper Darboux Integral is sometimes referred to as "not integrable" because there are certain functions that do not have a defined Upper Darboux Integral. This means that the Upper Darboux Integral cannot be used to calculate the area under the curve for these types of functions.
Functions that have discontinuities, such as the step function, are not integrable using the Upper Darboux Integral. Additionally, functions that have infinite oscillations or unboundedness are also not integrable using this method.
While there are some limitations to using the Upper Darboux Integral, it can still be a useful tool in certain situations. For example, it can provide a more accurate approximation of the area under a curve compared to other methods. It can also be used to calculate integrals of functions that are not continuous but have only a finite number of discontinuities.