Using a line integral to calculate area - Let C be a curve enclosing region R as described in Green's Theorem. If we choose P and Q such that : 1 then for the area of ду - dx region R we have A = 1dA = f, Pdx + Qdy. R de ду dP One possibility that results in = 1 is P(x, y) dx and Q(x, y) x. We then get the following formula for the area A : 2 -ydx + xdy. Use this formula to find the area enclosed by the ellipse : 1. Hint: parametrize the ellipse using trig. functions: what must x(t) and y(t) be in order for the equation of the ellipse to be cos? t + sin? t = 1?

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