Consider the unit circle $B$ and the unit square $S$ in the euclidean place where we have fix a Cartesian coordinate system.
Let $f(x,y)$ such that $f(x,y) = f(-x,-y)$ (even function).
If I know that $$ \int_S f(x,y) = 1 $$ can I deduce straightly (that is without integrate on $S\setminus B$ ) the constant $k$ such that $$ \int_B f(x,y) = k $$ ?