May 24th, 2013, 12:37 PM  #1 
Senior Member Joined: Jul 2012 Posts: 225 Thanks: 0  Find the potential function
Hi, here is the question and the solution, but there is something i did not understand, i'd like someone to explain to me. We are given the conservative vector field Find the potential function of the vector field. Solution: Where did C'(y) go??? Why?? 
May 25th, 2013, 01:17 PM  #2  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Find the potential function Quote:
Here, we must have and Quote:
The first is just while the second can be done integrating "by parts": let u= x, . The du= dx, and so the integral is equal to . Combining those, the integral, with respect to x, is . Plus a constant of integration, of course, but, here, since we were treating y as a constant, that "constant of integration" may be an arbitrary function of y: , just as your solution has. Quote:
Quote:
 
May 25th, 2013, 02:59 PM  #3 
Senior Member Joined: Jul 2012 Posts: 225 Thanks: 0  Re: Find the potential function
Got it, thanks again HallsofIvy 

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