Integrate[sqrt((2*r*Cos[t])^2 + (2rSin[t])^2 + 1)*r, {r,0,2},{t,0,2Pi}]

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.