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## Homework Statement

Use, using the result that for a simple closed curve

*C*in the plane the area enclosed is:

A = (1/2)∫(x dy - y dx) to find the area inside the curve x^(2/3) + y^(2/3) = 4

## Homework Equations

Green's Theorem:

∫P dx + Q dy = ∫∫

*d*Q/

*d*x -

*d*P/

*d*y

## The Attempt at a Solution

I solved the equation of the curve for x:

x = (4 - y^(2/3))^(3/2)

Also, from the original curve equation x^(2/3) + y^(2/3) = 4, when x = 0, y = +/- 8 because 4^(3/2) = 8.

But when I plug x = +/- (4 - y^(2/3))^(3/2) in for the x bounds and y = +/- 8 in for the y bounds in the resulting double integral

(1/2)∫∫ 2 dxdy

I have trouble integrating x = (4 - y^(2/3))^(3/2) it with respect to y.

Does anybody happen to know if there is a more correct way to solve this problem?

Thank you for your help!