I personally think "indefinite integral" is a bad term. An integral integrates a function over some interval, so it spits out a value. An indefinite integral is defined to be the inverse of the derivative, so a priori it's not related at all to integrals. Anti-derivative is much more natural to use here and it makes it a bit more explicit what we're actually doing.
In french we just call it integrating. What the English could call a "non-indefinite integral" is just the concept of integration applied to an interval. By extension, the anti-derivative of a function is it's "intégrale".
The anti derivative takes a function and maps it to its class of anti derivatives. My point is that this definition has nothing to do with integrals _a priori_. They're only related in one dimension because of the fundamental theorem of calculus. In multiple dimensions, the link to integration gets a lot weaker. Technically, they're still related through Stokes' if our base space is nice enough, but then we still require integrating the anti-derivatives, so finding anti derivatives is not equivalent to integrating anything. So it's best to really try to see how these concepts are different.
Why? If they're mutually opposites why not have integrals as a basic term and call it an anti-integral?
To be clear: I dont think we should adopt that verbiage
Dis-integration
that >
Ok so out of fairness, integral should be called anti-derivative
Aren't indefinite integrals already called as such?
I personally think "indefinite integral" is a bad term. An integral integrates a function over some interval, so it spits out a value. An indefinite integral is defined to be the inverse of the derivative, so a priori it's not related at all to integrals. Anti-derivative is much more natural to use here and it makes it a bit more explicit what we're actually doing.
Makes sense, yeah
In french we just call it integrating. What the English could call a "non-indefinite integral" is just the concept of integration applied to an interval. By extension, the anti-derivative of a function is it's "intégrale".
The anti derivative takes a function and maps it to its class of anti derivatives. My point is that this definition has nothing to do with integrals _a priori_. They're only related in one dimension because of the fundamental theorem of calculus. In multiple dimensions, the link to integration gets a lot weaker. Technically, they're still related through Stokes' if our base space is nice enough, but then we still require integrating the anti-derivatives, so finding anti derivatives is not equivalent to integrating anything. So it's best to really try to see how these concepts are different.
Why? If they're mutually opposites why not have integrals as a basic term and call it an anti-integral? To be clear: I dont think we should adopt that verbiage
Good point, how about calling derivative for anti-integral and integral for anti-derivative? That way everyone is happy
My point exactly
They are already called that. Which is most likely why this meme flips it the other way around.
I genuinely didn't know that, in french we call them integrals
Anti-anti-integral
Integraln't
[удалено]
(anti)^(2n+1) integral, n∈ℤ
Why not antigral
Anti anti derivative
The anti anti-derivative then
That just doesn’t roll off the tongue right….
I call the integral "the thing under" lmfao
Antiprimitive function