You should have a statement "a function is Riemann integrable if it is [...]" that helps with all a where it is integrable. For the rest you'll have to see how to show that it is not.Silviu said:I found at previous points a such that f is continuous, bounded and derivable, but I am not sure how to use that (as all these implications work just one way).
Riemann Integrability is a mathematical concept that describes the ability to calculate the area under a curve using a method called integration. It was developed by the German mathematician Bernhard Riemann in the 19th century.
The Riemann Integral is a specific type of integration technique that uses a series of rectangles to approximate the area under a curve. It is defined as the limit of a sum of areas of rectangles as the width of the rectangles approaches zero.
A function is considered Riemann Integrable if the upper Riemann sum and lower Riemann sum approaches the same value as the width of the rectangles approaches zero. This means that the function must be continuous on a closed interval and have a finite number of discontinuities.
Riemann Integrability is important because it allows us to calculate the area under curves and solve a variety of mathematical problems in physics, engineering, and economics. It also serves as the foundation for more advanced integration techniques in calculus.
Riemann Integrability has some limitations, such as being unable to integrate certain types of functions, such as those with infinite discontinuities or oscillating behavior. It also requires the function to be defined on a closed interval, which can be restrictive in some cases.