Question

Let f be integrable over R show that the funciton F defined by F(x) indefinite integral is properly defined and continuous is it necessarily lipschitz mathexchange?

Answer 1

Explanation:

A continuous function is one that has a set of unique solutions. a function is also said to be continuous if at every interval, there exist no sudden change in the assumed values otherwise the function will be discontinuous.

for example, the sine and cosine function are continuous over a set of real integers.

from the question, any assumed expression of x and integrating over the interval x and infinity will render the function continuous.

Assumed f(x) = cuberoot of x

Integrating and evaluating will prove that the function is continuous, as such a defined function is always a continuous function and not necessarily lipschitz.