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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
What is the integral of 1 x? - Mathematics Stack Exchange Answers to the question of the integral of $\frac {1} {x}$ are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers
What is the difference between an indefinite integral and an . . . Wolfram Mathworld says that an indefinite integral is "also called an antiderivative" This MIT page says, "The more common name for the antiderivative is the indefinite integral " One is free to define terms as you like, but it looks like at least some (and possibly most) credible sources define them to be exactly the same thing
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
calculus - Finding $\int x^xdx$ - Mathematics Stack Exchange How do you know it's legal to switch the summation and the integral? I know you can do it with finite sums but I thought there were certain conditions under which it invalid to switch them
When does a line integral equal an ordinary integral? One possible interpretation: a "normal" integral is simply a line integral where the path is straight and oriented along a particular axis Thus, as soon as you perform a transformation to the integrand to make the path straight and oriented properly, you're back at a "regular" integral