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Homework Statement
Given the polar curve [itex]r = 3\sqrt{\cos{2\varphi}},\ -\frac{\pi}{4}\leq\varphi\leq\frac{\pi}{4}[/itex]. Find the area of the surface enclosed by the curve using line integral of the second kind.
Homework Equations
The Attempt at a Solution
According to Green's theorem: if [itex]F(x,y)[/itex] and [itex]G(x,y)[/itex] are continuous on a smooth closed graph ([itex]r(\varphi)[/itex] in this case), then [itex]\oint_L F(x,y)\mathrm{d}x + G(x,y)\mathrm{d}y = \iint_D G_x(x,y) - F_y(x,y)\mathrm{d}x\mathrm{d}y[/itex].
The textbook, however, is very ineloquent as to what exactly [itex]F[/itex] and [itex]G[/itex] are and there are no examples given with polar curves. Do I have to parameterize the curve? I don't understand.
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