What does it mean for an integral to be convergent? The noun phrase "improper integral" written as $$ \int_a^\infty f (x) \, dx $$ is well defined If the appropriate limit exists, we attach the property "convergent" to that expression and use the same expression for the limit
Can the integral closure of a ring be taken intrinsically? However, one "intrinsic integral closure" that is often used is the normalization, which in the case on an integral domain is the integral closure in its field of fractions It's the maximal integral extension with the same fraction field as the original domain
What is an integral? - Mathematics Stack Exchange A different type of integral, if you want to call it an integral, is a "path integral" These are actually defined by a "normal" integral (such as a Riemann integral), but path integrals do not seek to find the area under a curve I think of them as finding a weighted, total displacement along a curve