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To: stephenjohnbanker; Irish_Thatcherite
The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits are functions of the differential variable,
partial/(partialz)int_(a(z))^(b(z))f(x,z)dx==int_(a(z))^(b(z))(partialf)/(partialz)dx+f(b(z),z)(partialb)/(partialz)-f(a(z),z)(partiala)/(partialz).

It is sometimes known as differentiation under the integral sign.

This rule can be used to evaluate certain unusual definite integrals such as

phi(alpha)==int_0^piln(1-2alphacosx+alpha^2)dx==2piln|alpha|

for |alpha|>1 (Woods 1926).

Feynman (1997, pp. 69-72) recalled seeing the method in Woods (1926) and remarked "So because I was self-taught using that book, I had peculiar methods for doing integrals," and "I used that one damn tool again and again."

852 posted on 01/02/2006 11:00:20 AM PST by NicknamedBob (How can I compete in a world of Cat 5 and wireless when my brain is wired by knob and tube?)
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To: NicknamedBob
"I used that one damn tool again and again."

I think I'll put a square wave into an integrator...

855 posted on 01/02/2006 11:11:25 AM PST by Irish_Thatcherite (~~~A vote for Bertie Ahern is a vote for Gerry Adams!~~~)
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