Use Green's theorem to evaluate the given double integral by means of a line integral.\\ (a) $\iint_R x^2 dA$, where $R$ is the region bounded by the ellipse $4x^2 + 9y^2 = 36$\\ (b) $\iint_R [1 - 2(y - 1)] dA$,
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The equation of the ellipse is 4x + 9y^2 = 36. We can rewrite this as x = (36 - 9y^2)/4. Now, let's find the partial derivatives of x and y with respect to x and y, respectively. ∂x/∂x = 1 ∂y/∂x = 0 ∂x/∂y = -9y/2 ∂y/∂y = 1 Using Green's theorem, the line Show more…
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