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Vector Calculus Concepts

Hi, I cannot figure this problem out. I would like to see how to work it. The answer in the book is 3/e, but I cannot get it. There must be a trick involved (hence the author's hint to think carefully), but I'm not sure what it is. I attached the problem. Thanks

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Hi there!
I must confess that at first this problem got me bamboozled as well. I thought maybe we should use the curl theorem or something like that, to evaluate the curl of teh field on an area that we can calculate teh path ...

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This solution is comprised of a detailed explanation to solve vector calculus.

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