#disgorgeengorge

[maths-help]

According to Green's theorem, we have:

Let  L = x3   and M = y3    

By applying Green's theorem to ∫(y3dx-x3dy) we'll find:

∫(y3dx - x3dy) = ∫∫(3y2 +9x2)dxdy

Which means:

∫(y3dx - x3dy) = ∫3y2dy∫9x2dx

We have ∫3y2dy = y3

And ∫9x2dx = 3x3

Which mean ∫(y3dx - x3dy) = 3x3y3

In the other hand the circle's equation gives us the limits of integration as -2 ≤ y ≤ 2 and -2 ≤ x ≤ 2 

∫(y3dx - x3dy) = 3[(2)3 - (-2)3][(2)3 - (-2)3] = 768

I hope this helps.

-Nidal