/sci/ - Science & Math

>>11272525
You can define most inverse functions by integrals

>>9484220

>>7115618
>so what's the point of the class

To learn how to integrate common classes of tricky integrals, series methods, and coordinate changes.

>"you'll get as good as you're going to get at solving integrals in calculus b, and that won't even be very good"

Because most functions can't be integrated in terms of common functions. Not because we never integrate.

>do working mathematicians and physicists solve their own integrals or do they just do them in mathematica or maple

Mathematicians invent and study special functions which are the functions (or inverses of functions) of unsolvable integrals:

ln(y)=<span class="math">∫_1^y dx/x[/spoiler]
J_n(y)=∫cos(n*x-y*sin(x))dx "Bessel function"
gd(x)=∫sech(x)dx "Gudermannian function"
erf(x)=<span class="math">2/√π∫_0^x e^{-t^2}dt[/spoiler] "error function"
Γ(t)=<span class="math">∫_0^∞ x^{t-1}e^{-x}dx[/spoiler] "gamma function aka (t-1)!"

>>6896794

>The sum of twin, cousin, and sexy primes is infinite

Does anyone know the name/proof of this theorem?

>>6544446
They're defined as the inverse function of special integrals