Question

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

I did u sub u = x^3 + 1
and got 26/9 as an answer? is that correct? :3

Answer 1

Yes. That is what I got as well. Evaluation at the limits gives
$$
3-\cfrac{1}{9}=\cfrac{27-1}{9}=\cfrac{26}{9}
$$

Answer 2

ok, thank you! :)

Answer 3

you're welcome