An integrable function is a mathematical function that can be integrated, or the area under its curve can be calculated, using various techniques such as the Riemann integral or Lebesgue integral.
A continuous function is a function that is defined and has no breaks or jumps in its graph. An integrable function, on the other hand, can have discontinuities or breaks in its graph but can still be integrated using specific techniques.
No, not all functions can be integrated. For a function to be integrable, it must satisfy certain conditions, such as being bounded and having a finite number of discontinuities.
Integrable functions have various applications in fields such as physics, engineering, economics, and statistics. They are used to calculate areas, volumes, and other quantities that have practical significance in these fields.
There are several methods for determining if a function is integrable, such as using the Riemann integral or Lebesgue integral. In general, if a function satisfies certain conditions, it can be considered integrable.