If the joint probability density of X and Y is given by f(x,y) = { 24xy for 0<x<1, 0<y<1, x+y<1

0 elsewhere

find P(X + Y < 1/2).

I did the integral from 0 to 1/2 of the integral from x to (1/2 - x) of f(x) dy dx. Are my integrals correct? After the first integration, I get the integral from 0 to 1/2 of 12 xy^2 dx evaluated from x to (1/2 - x), which is the integral from 0 to 1/2 of (3x - 24x^3)dx. That equals (3/2x^2 - 6x^4) evaluated from 0 to 1/2 which = 0. What am I doing wrong? Sorry I don't know how to write it out using the actual math symbols.