Hi.
In some cases when dealing with vectofields an such the are integral has to be expressed in terms of r(t).
the general form for r is r^2=(r*cos(t)-a)^2+(r*sin(t)-b)^2, When I solve this in maple it seems like I get the inverse of the desired result.
If I knew that was always the case I could just inverse my result to get the right expression for r, but im not sure if it only applies for this particular cas or all cases.
I would be happy if anyone took a quick look and suggested a way to obtain the desired solution for any center (a,b) for the circle.
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Expression for radius, circle centred at (a,b)
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(1) |
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(2) |
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![eval(%, [a = -1, b = 0])](/view.aspx?sf=220294_question/099fb7dc4be20ea3e89e2cddeb555437.gif)
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(3) |
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![plot3d([-2*x, x^2+y^2], y = -sqrt(-x^2-2*x) .. sqrt(-x^2-2*x), x = -2 .. 0, color = [green, red], orientation = [0, 0, 0])](/view.aspx?sf=220294_question/fbb621831b654fb71376715a06d48060.gif)
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(4) |
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![Area_off_center = int(r, [r = 0 .. -2*cos(t), t = (1/2)*Pi .. 3*Pi*(1/2)]); 1; Area_at_center = int(r, [r = 0 .. 1, t = 0 .. 2*Pi])](/view.aspx?sf=220294_question/a503ef7033b9feb9bcd983216f44c63c.gif)
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(6) |
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Download parametrization_of_r_not_centred_at_orgin.mw
I would also happily like to know how I can solve for the range r can take, obviously in the example i´m working with here r starts at 0, but that is not always the case i guess.
Thank you, your help is much apperciated
