Answer
$12$
Work Step by Step
Formula to calculate the arc length is: $l=\int_p^q \sqrt {1+[f'(x)]^2} dx$
Now, $l=\int_0^3 \sqrt {1+[x(x^2+2)]^2}dx=\int_0^3 (x^4+2x^2+1) dx$
Since, we know $\int x^n dx=\dfrac{x^{n+1}}{n+1}+C$
Then, $\int_0^3 (x^2+1) dx= [\dfrac{x^3}{3}+x]_0^3=\dfrac{27}{3}+3=12$