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What is the average value of [tex] y = x^{2}\sqrt{x^3+1} [/tex] on the interval [0,2] ?

Okay, so another average value problem right?

[tex] f(b) - f(a) = f'(c)(b-a) [/tex]

[tex] f(2) - f(0) = 2f'(c) [/tex]

[tex] 12 = 2f'(c) [/tex]

So then the average value is 6 right?