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True or false questions about line/surface integral

by zhuyilun
Tags: integral, line or surface
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Dec1-09, 08:16 PM
P: 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
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Dec2-09, 05:07 AM
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PF Gold
P: 39,552
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 [itex]\int f(x) dx[/itex].

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