In this case, `b-a=1`, so to find the average value, we simply need to evaluate:


Observing the graph, we notice that it has value near 0 for most values of x between 0 and 1. We estimate the value of the average to be somewhere around y = 0.5.


Put `u=3x^2-1`, then `du = 6x dx`

So `(du)/6=x\ dx`








So the average value required is `0.625` units. This is consistent with our earlier estimate.