Question: Use the Greens Theorem area formula given above to find the areas of the regions enclosed by the curves The astroid r(t) = (cos 3

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

The astroid r(t) = (cos³ t)i + (sin³ 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 Green's Theorem Area Formula Area of R - 1 2 x dy

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

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

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