average value = (Gb -Ga) / (b -a)

g(x) = (x^2)sqrt(1 +x^3), [0,2]

(Gb -Ga) = INT.(0-->2)[(1 +x^3)^(1/2)](x^2 dx)

= INT.(0-->2)[(1 +x^3)^(1/2)](x^2 dx)(3/3)

= (1/3)[(2/3)(1 +x^3)^(3/2)]|(0-->2)

= (2/9)[(1 +2^3)^(3/2) -(1 +0^3)^(3/2)]

= (2/9)[(9)^(3/2) -(1)^(3/2)]

= (2/9)[27 -1]

= 52/9

(b -a) = 2 -0 = 2

So, average value is (52/9) /2 = 26/9 = 2.889 -------answer.