Question

Proof for fundamental theorem for line integral? I don't get how to use chain rule to proof this theorem

Answer 1

\[\int\limits_{b}^{a} \frac{ \partial f }{ \partial x } \frac{ dx }{dt } +\frac{ \partial f }{ \partial y } \frac{ dy }{dt }+\frac{ \partial f }{ \partial z } \frac{ dz }{dt } dt\]

Answer 2

that's what I got up to, but I don't get how they used chain rule to get

Answer 3

integration of d/dt (f(rt)) dt from b to a

Answer 4

that integral above was suppose to be from b to a

Answer 5

See
http://tutorial.math.lamar.edu/Classes/CalcIII/FundThmLineIntegrals.aspx

Answer 6

That's the site I'm using I don't how he just used chain rule though

Answer 7

Did you look at his explanation for the chain rule
http://tutorial.math.lamar.edu/Classes/CalcIII/ChainRule.aspx

Answer 8

yes, that example uses x so it makes sense that dx/dx cancels but in this case its in terms of dt

Answer 9

Oh nvm I think I reasoned it out

Answer 10

thanks for our help