True or false questions about line/surface integral

[zhuyilun]

Homework Statement

if f has a continuous partial derivatives on R^3 and c is any circle ,then the integral of gradient f dot dr over c is zero

integral of f(x,y) ds over -c= - integral of f(x,y) ds over c

Homework Equations

The Attempt at a Solution

if the condition is not mentioned, then that statement is usually wrong
so i guess the second one is wrong
not quite sure about the first one

 

[HallsofIvy]

For (1), think about "Green's theorem". Does it apply here?

For (2), the "conditions" are that the function be integrable. Which it is because the question give $\int f(x) dx$.