Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

calculus

How does

compare with

?

How about

and

?

I'm *guessing* the second two are equal but the first two aren't, but is there a proof of this?

thanks

Last edited by Identity (2009-11-22 13:58:25)

gckc123

Member

Registered: 2009-10-19

Posts: 15

Re: calculus

The second one is equal only when certain conditions are met because you are interchanging lim and integration sign, which is not always valid.
Here is a theorem I find in a book (The elements of integration by Bartle)

Suppose that for some t_0 in [a,b], the function x-> f(x, t_0) is integrable on R, that

exists on R x [a,b], and that there exists an integrable function g on R such that

Then

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Maths is fun!

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: calculus

Thanks gckc123!