Question

onsider the function ?(?,?)=(3?2 +6??−2?2)?+(3?2 −4??+3?2)?. a) Without finding a potential function, show how you can...

onsider the function

?(?,?)=(3?2 +6??−2?2)?+(3?2 −4??+3?2)?.

a) Without finding a potential function, show how you can tell that that any line integral

∫ ?(?, ?) ∙ ?? ?

Page 5

along any curve C is independent of the path between the endpoints of C for the function F given above.

  1. b) Find the potential function associated with the F given above.

  2. c) Use that potential function to evaluate the line integral of F along the curve C which is the

    part of the ellipse ?2 + ?2 = 1 which lies in the first quadrant and goes from the point on the

    x-axis to the point on the y-axis.

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