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    Line integrals and rectangles

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    Line Integrals

    Please see the attached. Please do the problem(s) in detail and show all work.
    This question requires a line integral around the rectangle defined by the points (1,-1), (1,1), -1,1), (-1,-1) and with the function given. This defines 4 integrals that have to be evaluated as described in the problem.

    © BrainMass Inc. brainmass.com October 10, 2019, 6:51 am ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/line-integrals-rectangles-558998

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    I = Integral(C) [((x-a).dy - y.dx)/((x-a)^2 +y^2)] = I1 + I2 + I3 + I4

    where,

    I1 = Integral(y=-1 to y =1) [(1-a) . dy / ((1-a)^2 +y^2)] (Because, x = 1)

    I2 = Integral(x=1 to x=-1) [ - dx / ((x-a)^2 +1)] (Because, y = 1)

    I3 = Integral(y = 1 to y = -1) [ (-1-a) . dy / ((-1-a)^2 +y^2)] (Because, x = -1)

    I4 = Integral(x=-1 to x=1) [ dx / ((x-a)^2 + 1)] (Because, y = -1)

    Solution:
    I1 = (1-a) . (1/(1-a)) . tan-1( y / (1-a) ) | (y=-1 to y = 1)

    = tan-1( 1 / (1-a) ) - tan-1( -1 / (1-a) ...

    Solution Summary

    An integral along a rectangle of a function is solved in the solution.

    $2.19