Hello,

plz try to do these questions.

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- Jan 25th 2007, 10:19 AMm777Divergence Theorem, vector fields ..........
Hello,

plz try to do these questions. - Jan 25th 2007, 10:41 AMThePerfectHacker
Let me try...

First we need to find,

And is a box.

Thus,

Thus,

Thus,

Thus,

- Jan 25th 2007, 10:54 AMThePerfectHacker
Question 2]

You are given,

To determine if it is conservative for well-behaved vector fields the necessary and sufficient conditions is to check if

Thus, the we have,

Thus if is.

It turns out that there is an easier way in the special case for two dimension vector fields.

Necessary and suffient for well-behaves fields,

Called the "cross-partials test"

(If you taken Differencial Equations you will note it is the same test to determine if a differencial equation is exact or not).

In this case,

Thus, it is conservative.