In this question we will generalize the notions of even and odd, and
show multivariable analogs of single variable results. Let \(r>0\) and set
\(R = \left\{ (x,y) \in \mathbb R^2: -r \leq x,y \leq r\right\}\).
- Let
\(f\) be an integrable function such that \(f(-x,-y) = -f(x,y)\). Show that
\[ \displaystyle \iint_R f(x,y) dx dy = 0. \]
- Let \(f\) be an
integrable function such that \(f(x,-y) = -f(x,y)\). Show that \[
\displaystyle \iint_R f(x,y) dx dy = 0. \]