Find the area enclosed by the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (Using green's Theorem)
I am confused why we didn't use double integral here although answer makes sense without using double integral but I really don't understand why .
Find the area enclosed by the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (Using green's Theorem)
I am confused why we didn't use double integral here although answer makes sense without using double integral but I really don't understand why .
It may have helped you see the connection to the (typical) formal statement of Green's Theorem---as relating a double integral over $D$ to a line integral around the bounding curve of $D$---if they would have written the double integral first and then converted that to the line integral they began with. But alas...
See (3) here or the explanation here for why your text started with the integral they did.