The joint density function of X and Y is $f_{XY}(x,y)=\begin{cases}x+y & \text{for } 0<x<1, 0<y<1 \\ 0 & \text{elsewhere}\end{cases}$ then $P(X<2Y)$ is
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If the region of integration is complex, check if calculating the complement $P(X \ge 2Y)$ is simpler. In this case, both are relatively straightforward, but always ensure your limits correctly reflect the intersection of the inequality and the density's support.