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Double Integral Limits for a Sideways Rectangle

  1. Nov 21, 2008 #1
    1. The problem statement, all variables and given/known data
    I have to solve the integral of (ytan^-1(x) - 3) inside the area of the rectangle with vertices (1,0), (0,1), (2,3), (3,2). How do I set up these limits?

    2. Relevant equations
    This is a tilted rectangle so I can't use just values for the limits?

    3. The attempt at a solution
    This is a Green's theorem problem that started out as integral(tan^-1(x)dx + 3xdy). I just can't figure out the limits.
  2. jcsd
  3. Nov 21, 2008 #2


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    The parallel lines through (1,0), (3,2) and (0,1),(2,3) are y= x-1 and y= x+ 1, respectively; both are variations on "y-x= constant". The parallel lines through (1,0),(0,1) and (3,2),(2,3) are y= 1-x and y= 5-x, respectively; both are of the form "y+ x= constant. Changing variable to u= y- x and v= y+ x gives an integral with limits of integration in u of -1 to 1 and in v, 1 to 5. Be sure to calculate the Jacobian to convert dxdy.

    Have you already calculated the integration around the boundary?
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