- #1

LCSphysicist

- 646

- 161

- Homework Statement
- I am having a little trouble to see how the changes of variables works here.

- Relevant Equations
- Functionals.

Be ##x = x(u,v) y = y(u,v)##, if ##F = \int f(x,y,y')dx## and the Jacobian's determinant different of zero, ##v = v(u)##

##{\Large {J = \int F[x,y,y']dx ---> \int F[x(u,v),y(u,v),\frac{y_{u} + y_{v}v'}{x_{u} + x_{v}v'}](x_{u} + x_{v}v')du}}##

The last term in the bracket is confusing me, how to get it?

##{\Large {J = \int F[x,y,y']dx ---> \int F[x(u,v),y(u,v),\frac{y_{u} + y_{v}v'}{x_{u} + x_{v}v'}](x_{u} + x_{v}v')du}}##

The last term in the bracket is confusing me, how to get it?