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When Is Function Integrable?

James H. Sterling • • 6 min read
When Is Function Integrable?

In practical terms, integrability hinges on continuity: If a function is continuous

function is continuous
In mathematics, particularly in operator theory and C*-algebra theory, a continuous functional calculus is a functional calculus which allows the application of a continuous function to normal elements of a C*-algebra.
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on a given interval, it's integrable on that interval. Additionally, if a function has only a finite number of some kinds of discontinuities on an interval, it's also integrable on that interval.

What makes a function non integrable?

The simplest examples of non-integrable functions are: in the interval [0, b]; and in any interval containing 0. These are intrinsically not integrable, because the area that their integral would represent is infinite. There are others as well, for which integrability fails because the integrand jumps around too much.

Is a integrable function?

In mathematics, an absolutely integrable function is a function whose absolute value is integrable, meaning that the integral of the absolute value over the whole domain is finite. , so that in fact "absolutely integrable" means the same thing as "Lebesgue integrable" for measurable functions.

James H. Sterling
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James H. Sterling

James Sterling reports on renewable energy developments, climate policy, ecological conservation, and green tech innovations around the globe.