The curve $\displaystyle C$ has equation

$\displaystyle y =\frac{1}{2}x^2$.

a] use the substitution $\displaystyle x=sinhu$ to evaluate the arc length of $\displaystyle C$ correct to 2 decimal places.

b] The arc of $\displaystyle C$ joining the points $\displaystyle (0,0)$ and $\displaystyle (2,2)$ is rotated through four right angles about the x-axis. Find the area of the curved surface generated correct to 2 decimal places.

I've done part a] - got 2.96.

Part b] is giving me significant trouble though. I write the integral as

$\displaystyle 2\pi \int_0^2 \frac{1}{2}x^2 \sqrt{1+x^2} dx$ and from here, I've tried a variety of techniques - I made the $\displaystyle x^2$ term into $\displaystyle \sqrt{x^4}$ and used the rule $\displaystyle \sqrt{a} . \sqrt{b} = \sqrt{ab}$ but the answer was wrong, and I tried the same hyperbolic substitution, which also gave me a wrong answer. I know this because the answer is written down on a sheet with no working to show it was obtained. Please could you suggest a suitable way to approach the question? Any help is greatly appreciated