Finding Integral Over [0,2pi] with Square Root Function

[Alexx1]

I have to find: \int_{0}^{2\pi}\sqrt{t^2+2} dt

I found that \int \sqrt{t^2+2} dt = \frac{t\sqrt{t^2+2}}{2} - arcsin(\frac{t}{\sqrt{2}}) + c

But when I fill in 2\pi I get: \frac{2\pi \sqrt{4\pi ^2+2}}{2}- arcsin(\frac{2\pi }{\sqrt{2}})

but arcsin(\frac{2\pi }{\sqrt{2}}) doesn't exist..

Have I done something wrong?Problem solved!

 

[Dick]

I think you mean arcsinh rather than arcsin, don't you?