Line integrals and paths with the same endpoints

[Aaronc]

Homework Statement

Suppose that p and q are points in U, where U is an open, path-connected, simply connected subset of Rn and c1 and c2 are smooth curves in Rn with c1(0)=c2(0)=p, c1(1)=c2(1)=q. Let w be a 1-form on U. Prove that the line integral of w over c1 equals the line integral of w over c2.

Homework Equations

simply connected means every closed curve homotopes to a point



I don't know where to start :(

 

[Ray Vickson]

Homework Statement

Suppose that p and q are points in U, where U is an open, path-connected, simply connected subset of Rn and c1 and c2 are smooth curves in Rn with c1(0)=c2(0)=p, c1(1)=c2(1)=q. Let w be a 1-form on U. Prove that the line integral of w over c1 equals the line integral of w over c2.

Homework Equations

simply connected means every closed curve homotopes to a point



I don't know where to start :(

Reading your textbook or lecture notes would be a good place to begin.

RGV

 

[HallsofIvy]

You might start with the definition of "one-form". And do you know what an "exact differential" is? It looks to me like the statement you are trying to prove is NOT true unless there are some other conditions.