Principle of Differentiation and Integration query

Hi Folks,

if we have an implicit function eqn1

then we can find the standard derivative eqn 2 and

the partial derivative eqn3

However, I am trying to grasp the idea of having a standard/total derivation and partial derivation of functions as above yet we dont have standard or partial integration (ie the reverse). How is that?

If we integrate back eqn2 wrt to x we get eqn1 with a constant. This constant can be determined if BC's or IC's are known (ie 6) etc...but

if we integrate eqn3 wrt x we can get eqn1 with a constant also but we lose the term. How does one get this term back?

I dont think I understand this fully. Can anyone shed some light?

Thanks

Bugatti79

Principle of Differentiation and Integration query

Quote:

Originally Posted by

**Ackbeet** I'm saying that if I were given

,

and told to integrate with respect to x, I would produce the following:

Just when I thought I understood!! (Headbang)

Integrating dz/dx, I get for each term

the dx's cancel

How does the third term go to 0 because I get

the dx's cancel

All of these term plus a constant etc. However, I now have two '5xy' terms. Should only have one. What have i done wrong?

I feel stupid now (Happy)

Thanks

Principle of Differentiation and Integration query

Quote:

Originally Posted by

**Ackbeet** The third term doesn't go to zero. I think you're going to see some interaction between terms there. You have to combine the last two terms, I think:

which just becomes ...

think that makes sense. Thanks