The exercise consists of two parts, and I'm supposed to solve it without doing any calculations. The first is to integrate the function on $D_1$ where $D_1$ is the square $-1\leq y \leq 1, -1 \leq x \leq 1$. Since, for an odd function $f$, $\int^{a}_{-a} f(x) \text{ dx} = 0$, I can simply apply this and infer that $\int^{-1}_1y^{101} \text{ dy} \int^{-1}_1x^{71} \text{ dx} =0$.
I believe that I am supposed to do the same when integrating $f$ over $D_2$, which is the circular disc $x^2 + y^2 \leq 1$, but I am unsure of how to slice $D_2$ in such a way that I can use this property of odd functions. Any help would be much appreciated.
Hint. Try to use the substitution $u=-x, v=-y$ and show that $I=-I$ if $I$ is the value of the integral.