- #1

jonjacson

- 453

- 38

If we have an expression like this one:

x + y = 2

And we have to differenciate it, there is an algorithm that tells us how to do it. We have to find the relationship between the differentials of the given functions. To find them we have to substract the infinitesimal increment of the function minus the function itself:

(x+dx) + (y+dy) - (x + y) = (2+0) -(2), Since 2 is a constant its differential is 0, we found:

dx + dy = 0

It is clear how the differentiation operation acts on every quantity on the equation.

But now we have this expresion:

dx + dy = 1

And we need to integrate it, I understand that we have to find the relation between y and x, whose differentials will make this equation correct. But it is not clear to me how to act on the number 1.

∫dx +∫dy = ∫1

On the left we get x+y + constant, but What happens on the right? Should we integrate on the variable x? Or should it be done on the variable y? How should we proceed?

Thanks!