Can't be done without knowing what [tex]f[/tex] is...
But I can tell you that the average value of [tex]f[/tex] is given by
[tex]\dfrac{\displaystyle\iint_Rf(x,y)\,\mathrm dx\,\mathrm dy}{\displaystyle\iint_R\mathrm dx\,\mathrm dy}[/tex]
At the very least, we can compute the denominator, which is just the area of [tex]R[/tex]. You have
[tex]\displaystyle\iint_R\mathrm dx\,\mathrm dy=\int_{x=0}^{x=1}\int_{y=x}^{y=1}\mathrm dy\,\mathrm dx=\int_0^1(1-x)\,\mathrm dx=\dfrac12[/tex]
so the average value will be
[tex]2\displaystyle\iint_Rf(x,y)\,\mathrm dx\,\mathrm dy[/tex]
