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From: John on 17 May 2010 11:37
Is there a substitution that converts the following integral (in the
url below) to the form of integral from a to b where a and b are real
numbers ?

http://img21.imageshack.us/img21/3156/screenshot2ou.png

Thanks
From: George Jefferson on 17 May 2010 19:23


"John" <to1mmy2(a)yahoo.com> wrote in message
news:e819eac7-486c-4344-a17f-df3934119367(a)q33g2000vbt.googlegroups.com...
> Is there a substitution that converts the following integral (in the
> url below) to the form of integral from a to b where a and b are real
> numbers ?
>
> http://img21.imageshack.us/img21/3156/screenshot2ou.png
>
> Thanks


Of course. The first integral is a function x alone as is the second
integral. Hence they must be equal(if the integrals are to be equal).

e.g.,

let g(x) = int(f(x,y),y=0..u(x))

then

int(g(x)*y,y=0..1) = g(x)*int(y,y=0..1) is one such solution

int(f(x,y),y=0..u(x)) = int(f(x,y),y=0..u(x))*int(v(y),y=a..b)

for any int(v(y),y=a..b) = 1 (and any function works because we can
normalize it)

and therefor,

int(f(x,y),y=0..u(x)) = int(int(f(x,y),y=0..u(x))*v(y),y=a..b) =
int(g(x)*v(y),y=a..b) = int(w(x,y),y=a..b)











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