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yes, every continuous function is integrable.

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15y ago

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Every continuous function is integrible but converse is not true every integrable function is not continuous?

That's true. If a function is continuous, it's (Riemman) integrable, but the converse is not true.


Do all functions have integrals?

No, all functions are not Riemann integrable


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In quantum mechanics, acceptable wave functions must be continuous, single-valued, and square-integrable. They must also satisfy the Schrdinger equation and have finite energy.


Let f be an odd function with antiderivative F. Prove that F is an even function. Note we do not assume that f is continuous or even integrable.?

An antiderivative, F, is normally defined as the indefinite integral of a function f. F is differentiable and its derivative is f.If you do not assume that f is continuous or even integrable, then your definition of antiderivative is required.


What has the author Krzysztof Ciesielski written?

Krzysztof Ciesielski has written: 'I-density continuous functions' -- subject(s): Baire classes, Continuous Functions, Functions, Continuous, Semigroups


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Not at all.Y = x2 is a continuous function.


Are all functions continuous?

No. Not all functions are continuous. For example, the function f(x) = 1/x is undefined at x = 0.


What function is integrable but not continuous?

A function may have a finite number of discontinuities and still be integrable according to Riemann (i.e., the Riemann integral exists); it may even have a countable infinite number of discontinuities and still be integrable according to Lebesgue. Any function with a finite amount of discontinuities (that satisfies other requirements, such as being bounded) can serve as an example; an example of a specific function would be the function defined as: f(x) = 1, for x < 10 f(x) = 2, otherwise


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Yes, all polynomial functions are continuous.


Can all functions be discrete or continuous?

No. There are many common functions which are not discrete but the are not continuous everywhere. For example, 1/x is not continuous at x = 0 (it is not even defined there. Then there are curves with step jumps.


What has the author Jean Schmets written?

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What is a spectral curve?

A spectral curve is a mathematical concept used in the study of integrable systems, particularly in the field of integrable models in mathematical physics. It is a curve in the complex plane associated with a particular integrable system, providing information about the system's eigenvalues and other important properties. Spectral curves play a key role in understanding the dynamics and properties of integrable systems.