Joint continuous distribution

Jeg har en opgave, som lyder således:

Suppose that either of two instruments might be used for making a certain measurement. Instrument 1 yields a measurement whose pdf, h1, is: h1(x) = 2x; for 0 < x < 1, and zero otherwise. Instrument 2 yields a measurement whose pfd, h2, is: h2(x) = 3x2; for 0 < x < 1, and zero otherwise. Suppose that one of the two instruments is chosen at random and a measurement X is made with it.

a) Determine the marginal pdf of X: (Hint: Let Y be the choice of instrument.

f(x; y) = P(y = 1)h1(x) + P(y = 2)h2(x))

Jeg ved at jeg med dobbelt integration, kan finde den marginale pdf, men i denne her opgave har jeg det virkelig svært ved at gribe det an. 

Håber der er hjælp at hente..