The average value of a function over a region a < x < b is given by:

(f) = b ∫a (f(x)dx) / (b − a)  

The price of gold, P, increased from about $270 per ounce in 2001 to $1400 per ounce in 2011, roughly following a functional form given by P(t) = $270 + $11.3 yr^−2 t^2 where t is the time in years since 2001.

Using a definite integral, find the average price of gold in the two year period between t = 2 yr and t = 4 yr