Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Calculus

Hello.

I am a little confused about the whole dx, du etc notation. I have a couple of questions:

1. If you have ∫ y dx, does that mean multiplied by dx, or just 'with repect to x'?

2. Why, for example when you are integrating using substitution, can you split du/dx? In other words, if du/dx = 2x, why can you then say dx = du/2x? I thought du/dx was just a notation, not actually a fraction?

Thanks.

SvenBee

Member

Registered: 2008-03-08

Posts: 106

Re: Calculus

du, dx, dy... They are all notations representing "with respect to". But... when you get to the point where you are graphing the area under the curves they become interchangeable with Δx, Δy, Δu, etc. The variable being integrated (u in u substitution) has to be respected. For example: ∫u dx is nothing.  You cannot integrate or derive a function of one variable with respect to another. So in cases where it is used in u-substitution and swapped with dx it is treated like a variable itself.

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e...the red-headed stepchild of math.