Answer
$0$
Work Step by Step
Since $av(f)=\dfrac{1}{B-A}\int_{A}^{B} f(x) dx$
Here, we have
$av(f)=\dfrac{1}{\sqrt 3-0}\int_{0}^{\sqrt 3} (x^2-1) dx$
This implies that
$\dfrac{1}{\sqrt 3-0}[\dfrac{(\sqrt 3)^3-(0)^3}{3}-(\sqrt 3-0)]=0$