Suppose you have two continuous random variables \( X, Y \) with a joint pdf \( f_{X, Y} \). Then

\( \Pr\{X > Y\} = \iint\limits_{\{(x,y):x > y\}} f_{X,Y}(x,y)dxdy \)

\( = \int_{-\infty}^{+\infty} \int_y^{+\infty} f_{X,Y}(x,y)dxdy \)

\( = \int_{-\infty}^{+\infty} \int_{-\infty}^x f_{X,Y}(x,y)dydx \)