# True or false questions about line/surface integral

1. ### zhuyilun

27
1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. 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

2. ### HallsofIvy

40,544
Staff Emeritus
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 $\int f(x) dx$.