differentiate parameters under the integral sign

16: math/differentiate parameters under the integral sign:
"Surely You're Joking, Mr. Feynman!", p72:

That book [Woods`Advanced Calculus]
also showed how to
differentiate parameters under the integral sign
--it's a certain operation. It turns out
that's not taught very much in the universities;
they don't emphasize it.
But I caught on how to use that method,
and I used that one damn tool again and again.
So because I was self-taught using that book,
I had peculiar methods of doing integrals.

wolfram` Leibniz Integral Rule
[ tagged as Recreational Mathematics >
Mathematics in the Arts > Mathematics in Literature >
Surely You're Joking, Mr. Feynman! ]

Leibniz integral rule gives a formula for
differentiation of a definite integral whose limits are
functions of the differential variable,
It is sometimes known as
differentiation under the integral sign.

also known as:

differentiating under the integral sign,
differentiation with respect to a parameter,
or sometimes even Feynman Integration.

. see thorough review of related theorems;
see Goldmakher's applications of it .