QUESTION9(3) In this thesis we will use Green's theorem to calculate the area of an area. Greens Theorem Let R be a regular, closed area in the xy-plane so that the edge C consists of one or more piecewise smooth, simple and closed curves with a positive orientation in relation to R. If F = Fx(x, y) ] [Fy(x, y) ) is is a smooth vector field on R, then we have that F . dr = JJ OFy dA Ox ay OFY OF I = 1 If ay then we see that the right side above is reduced to be the area of area R. So we can use Green's theorem to calculate area. Areal av R = $ F . dr In particular, the area calculation of an area can be simplified by using one of the following vector fields F = F = |eller F = ] in the formula above Calculate the area of the area bounded by r (t ) = 2 cos' (t) for 12 sin? (t). Osts2It