- #1
gr3g1
- 71
- 0
The question is:
Show that the given integral is independent of the path.
F(x,y) = (2xy)dx + (x^2)dy
So i take the integral of 2xy w.r.t x and it gives:
x^2*y + g(y)
now I take the partial derivative of that function w.r.t to y and i get:
x^2 + g'(y)
I set it equal to (x^2)
so
x^2 + g'(y) = x^2
so g'(y) = 0
so i would integrate
x^2*y + 0
is that right?
Thank you
Show that the given integral is independent of the path.
F(x,y) = (2xy)dx + (x^2)dy
So i take the integral of 2xy w.r.t x and it gives:
x^2*y + g(y)
now I take the partial derivative of that function w.r.t to y and i get:
x^2 + g'(y)
I set it equal to (x^2)
so
x^2 + g'(y) = x^2
so g'(y) = 0
so i would integrate
x^2*y + 0
is that right?
Thank you