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Can someone point me to a reliable source (textbook, website) that teaches this technique? It seems like no course at my university covers this technique even though it is quite useful for solving particular integrals!
gnomedt said:Feynman mentions it in some of his literature, is this where you heard it? He read about the idea in Frederick Wood's Advanced Calculus, a now hard-to-obtain book, but a reasonably-sized library may have a copy. It does have a very good explanation of differentiation under the integral sign. If you can't find it though, pm me, and I can send you a copy of that part of the text. (I took pretty extensive notes at that part.)
Differentiating under the integral sign is a mathematical technique used to find derivatives of a function that is expressed as an integral. It involves taking the derivative of the function with respect to one of the variables in the integrand while keeping the other variables constant.
This technique is useful because it allows us to evaluate integrals that cannot be solved using traditional methods. It also provides a way to find derivatives of functions that cannot be expressed in closed form.
The steps for differentiating under the integral sign are as follows:
No, this technique can only be used for functions that are continuous and have a well-defined integral. It is also important to check for convergence of the integral before using this technique.
Yes, there are some limitations to this technique. It cannot be used for functions that have changing limits of integration. It also does not work for functions with multiple variables in the integrand, as the derivative would depend on which variable is being held constant.