Thanks again.
]]>let u= ln(x)
du/dx = 1/x or du = dx/x
replace dx/x with du
and ln(x) with u
then you are left with ∫ u du == u²/2
thats where the 2 comes from.
]]>0.5 ln x=ln (x^0.5)
]]>[Edit: the integral symbols that I pasted from the row above came through as ?, so that will have to do. all the ? below are intended to be integral symbols.]
Integrate (x) = ln(x) / x on the interval [1, 100].
So I go like this:
u = ln(x)
du = 1/x dx
?(u * du) = ln(x)dx ? ln|x|dx = u² ... what?
I'm stuck; I don't get it. The solution in the book goes like this:
? [b=ln100, a=ln1] udu ->
u² | ln100
2 | ln1 ->
(ln100)² / 2 - 0
I understand why the limits of integration changed from [1, 100] to [ln1, ln100], and that the final expression is g(b) - g(a), which as I understand it is the final step to definite integration.
What I don't understand is, where did the /2 come from?
Thanks for the help. I hope my explanation is clear; some notation really doesn't translate to the web at all.
]]>