Why is it that the constant = 0?

[flyingpig]

Homework Statement

a) Find a function f such that F = ∇f

b) Evaluate the line integral along the given curve

$$\mathbf{F}(x,y) = <x^3 y^4 , x^4 y^3>$$

C: $$\mathbf{r}(t) = <\sqrt{t}, 1 + t^3>$$ where $$t \in [0,1]$$


My question

I did everything else right, but my solution manual tells me that the constant i get when I find f is 0

Solutions
[PLAIN]http://img156.imageshack.us/img156/5149/unledoy.jpg

 

[lineintegral1]

You probably differentiated wrong or something similar. All you do is take the derivative of the potential function after you have integrated it in terms of x. Then you see if this matches the y component of your gradient. If they are the same, then the constant is zero. If they are not the same, then you integrate with respect to y.

 

[flyingpig]

You probably differentiated wrong or something similar. All you do is take the derivative of the potential function after you have integrated it in terms of x. Then you see if this matches the y component of your gradient. If they are the same, then the constant is zero. If they are not the same, then you integrate with respect to y.

No they said

g'(y) = 0

g(y) = 0y + K

g(y) = K

I don't understand how you can just take K = 0

 

[Mark44]

The problem says to "find a function f..."

All such functions are f(x, y) = (1/4)x⁴y⁴ + <some constant>

Since they're looking for just one, it's convenient to drop the constant.

 

[flyingpig]

The problem says to "find a function f..."

All such functions are f(x, y) = (1/4)x⁴y⁴ + <some constant>

Since they're looking for just one, it's convenient to drop the constant.

What?? What a stupid question (and stupid student i am...)