Wednesday, 29 October 2014

calculus - dx being a desginator (with respect to x) or being a term?

I am confused as to what dx truly is. I am doing some u-substitution problems and this is what I came across:



2x(x1)1/2dx




u=x1 and therefore du=1



when we substitute we get:
2(u3/2+u1/2)du
(here the du simply replaces the dx because our variable changed)



In another example:
4x5(x2+1)1/3dx
u=x3+1

du=3x2
therefore it becomes:
4(u1)(du/3)(u)1/3
-here my teacher didn't put dx at the end, she just left it off
So my question is this: why is it that sometimes dx and du are treated as values that can be multiplied to other terms in the integrand and sometimes they are simply treated as a command (do "blank" with respect to x, or u or whatever is used)?

No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...