Mass of $ A := \{ x \in R^2\ | x<y , y<2, y>1/x \}$

Question

How does one calculate the Lebesgue Measure of the above set?

I tried the following:

$ \lambda^2(A) = \int_{R^2} 1_A d(\lambda^2(x,y)) = \int_R\int_x^2 1_{ \{1/x < y\} } d\lambda(y)d\lambda(x)$

but then I have no idea how to reformulate the inequality $1/x < y $.