Final answer:
Green's theorem is used for Finding Areas, and in the case of an ellipse, it can be applied by choosing an appropriate vector field to simplify the area computation. The correct application of Green's theorem in this scenario is b) Finding Areas.
Step-by-step explanation:
The correct application of Green's theorem in the scenario of computing the area inside an ellipse is Finding Areas. Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D enclosed by C. For calculating the area of an ellipse, we can use Green's theorem by integrating over the region D with a chosen vector field that simplifies the calculations, such as F(x, y) = (0, x) or F(x, y) = (-y, 0). The area A of the region is given by the integral A = ½ ∫∫ (Pdx + Qdy), where P and Q are the components of the vector field.
Green's theorem relates a line integral around a simple closed curve to a double integral over the plane region bounded by the curve. In the case of finding the area inside an ellipse, Green's theorem allows us to convert the double integral over the region into a line integral around the boundary of the ellipse, which can then be evaluated to find the area.