Use the Green’s Theorem area formula given above to find the areas of the regions enclosed by the curves.

The ellipse r(t) = (a cos t)i + (b sin t)j, 0 ≤ t ≤ 2π

If a simple closed curve C in the plane and the region R it encloses satisfy the hypotheses of Green’s Theorem, the area of R is given by

The reason is that by Equation (4), run backward,

Transcribed Image Text:

Green's Theorem Area Formula Area of R - 1 2 x dy y dx