Respuesta :

LammettHash
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]

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