Folks,

Find a simple closed curve with counter clockwise rotation that maximizes the value of $\displaystyle \int_{C} \frac{1}{3} y^3 dx + (x-\frac{1}{3} x^3) dx$

If I apply greens theoremI calculate $\displaystyle \int \int_R (1-x^2-y^2) dA= \int_{0}^{2 \pi} \int_{0}^{1} (1-r^2)r dr d \theta = \frac{1}{2}$...?