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?