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Math Help - Compute the closed curve integral of F (dot) dR in two ways.....

  1. #1
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    Compute the closed curve integral of F (dot) dR in two ways.....

    Let C be the square with vertices (-1,0), (0,0), (0,1), and (-1,1). Let F=[ycos(x)]i -[y^3] j. Compute the closed curve integral of F (dot) dR in two ways:

    once using a double integral
    and once by summing four line integrals (one for the each edge of the square)

    Please help! I am really struggling
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  2. #2
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    Re: Compute the closed curve integral of F (dot) dR in two ways.....

    Evaluating using line integral:
    F.dr= ycos x dx - y^3dy
    C the boundary of the square = C1+C2+C3+C4
    Along each Ci, one of the variable x or y is a constant. Hence your integration becomes easy.

    Use Green's theorem to convert into double integral.

    Hope this helps!
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