Measure of region

Question

Let $\Omega:=[0,1]^2$, $f(x):=-x+1$ and $g(x):=(x-1)^2$. I am supposed to compute the $L^2$ measure of the area of the region given by $$M:=\{(x,y)\in\Omega\;|\;g(x)\leq y\leq f(x)\}.$$ Can I just compute $$\mathcal{L}^2(M)=\int_{0}^{1}f(x)^2dx-\int_{0}^{1}g(x)^2dx$$ in this case, or what is meant by the $L^2$ measure of a region?

Answer 1

The symbol $L^2$ probably stands for "two-dimensional Lebesgue measure". One usually writes it in script: $\mathcal{L}^2$.