My Math Forum Integral total and partial of a function?

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 March 31st, 2014, 02:48 AM #1 Senior Member   Joined: Nov 2013 Posts: 137 Thanks: 1 Integral total and partial of a function? Like we have the total differential of a function: I was thinking, why not take the "total integral" of a function too? Thus I did some algebraic juggling and, how I haven't aptitude for be a Ph.D. in math, I bring my ideia for the experients from here evaluate... Anyway, the ideia is the follows: Let y = f(x), so: $\int y dx= \int f dx$ $\int y \frac{dx}{dx}= \int f \frac{1}{dx}dx$ $\int y= \int f \frac{1}{dx}dx \;\;\;\Rightarrow \;\;\; \int y du = \int f \frac{du}{dx}dx$ Generalizing... Let w = f(x,y,z), so: $\int w= \int f \frac{1}{dx}dx + \int f \frac{1}{dy}dy + \int f \frac{1}{dz}dz$ I don't venture take the 2nd integral of y because I think that will arise one d²x in the denominator... What you think about? All this make sense?
 March 31st, 2014, 01:07 PM #2 Global Moderator   Joined: May 2007 Posts: 6,528 Thanks: 589 Your "integrals" are strange. You need a differential to make sense.
March 31st, 2014, 06:35 PM   #3
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Joined: Nov 2013

Posts: 137
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Quote:
 Originally Posted by mathman Your "integrals" are strange. You need a differential to make sense.
If you to multiply $\displaystyle \int w$ by a desired differential, it will make sense...

 April 1st, 2014, 03:46 PM #4 Global Moderator   Joined: May 2007 Posts: 6,528 Thanks: 589 It looks to me that your last equation says 1 = 3.

 Tags function, integral, partial, total

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