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# Are continuous functions integrable

Updated: 4/28/2022

Wiki User

14y ago

yes, every continuous function is integrable.

Wiki User

14y ago

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Q: Are continuous functions integrable
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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

### 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

### Are all continuous functions linear?

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.

### Are all polynomial funcions continuous?

Yes, all polynomial functions are continuous.

### 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 &lt; 10 f(x) = 2, otherwise

### 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?

Jean Schmets has written: 'Spaces of vector-valued continuous functions' -- subject(s): Continuous Functions, Locally convex spaces, Vector valued functions

### What has the author Frederick Bagemihl written?

Frederick Bagemihl has written: 'Meier points and horocyclic Meier points of continuous functions' -- subject(s): Continuous Functions

### Is a corner continuous?

Yes, a corner is continuous, as long as you don't have to lift your pencil up then it is a continuous function. Continuous functions just have no breaks, gaps, or holes.