integrating ln(y) w.r.t x

• Feb 22nd 2011, 06:34 AM
Plague01
integrating ln(y) w.r.t x
I was looking at the thread where this person list the methods for differential equations. In the exact equation part, he appears to integrate ln(y) with respect to x and obtain xln(y). How do you do this?
• Feb 22nd 2011, 06:39 AM
Prove It
Since it is being integrated w.r.t. $\displaystyle x$, $\displaystyle \ln{y}$ is treated as a constant.

What's the integral of a constant?
• Feb 22nd 2011, 06:59 AM
Plague01
Quote:

Originally Posted by Prove It
Since it is being integrated w.r.t. $\displaystyle x$, $\displaystyle \ln{y}$ is treated as a constant.

What's the integral of a constant?

x multiplied by the constant. ahh thanks very much. On a side note, when you differentiate say xy, you do not treat y as a constant. You get y+x(dy/dx). Is that because your treating y as a function of x?
• Feb 22nd 2011, 07:21 AM
DrSteve
That is implicit differentiation. If y is a function of x, then that is how you would take the derivative.
• Feb 22nd 2011, 07:24 AM
Prove It
In this case, you are treating integration as the opposite of PARTIAL differentiation...
• Feb 22nd 2011, 07:48 AM
Plague01
Quote:

Originally Posted by Prove It
In this case, you are treating integration as the opposite of PARTIAL differentiation...

I'm not sure why when you are only dealing with 2 variables, x and y.