If I know that a vector is conservative, and I want to find it's potential, is there an easy way to do it, other than guess and check? (the method in my book doesn't make any sense!) For example, I know that is conservative, how would I find its potential?

Question

If I know that a vector is conservative, and I want to find it's potential, is there an easy way to do it, other than guess and check? (the method in my book doesn't make any sense!)   For example, I know that <6x +5y, 5x+4y> is conservative, how would I find its potential?

anonymous · Answer

http://tutorial.math.lamar.edu/Classes/CalcIII/ConservativeVectorField.aspx This is a nice page. Scroll to example 3.

anonymous · Answer

take integral w.rt x, y  and add the terms together
integral of 6x +5y wrt. to x  is 3x^2+5yx 
integral of 5x +4y wrt. to y is  5xy+2y^2
put the terms together(taking common term only once)
3x^2+ 5xy+2y^2