Arc Length of Curve r(t) from 0 to 1: Find the Integral

[SummerPhysStudent]

Ok, So i need to find the arc length of the curve r(t) = < 2t, e^t, e^(-t)> from 0<=t<=1
so L should be the integral from 0 to 1 over the magnitude of r'(t) dt. So what I'm getting is
S₀¹ sqrt(4 + e^2t + e^-2t)dt
and this I'm not sure how to do this integral. Anyhelp?

 

[e(ho0n3]

You can use Latex to type up the integral instead of using that weird S. You might want to check what |r'(t)| dt is again. The integral you'll get won't be pretty though.

 

[homology]

For whatever its worth, I chucked the integral into Mathematica and it didn't solve it.

Oh, wait, well if we screw around with the integral to get

$$\int_{0}^{1}\sqrt{4+2(\frac{e^2t + e^-2t}{2})}dt=\int_{0}^{1}\sqrt{4+2cosh(2t)}dt$$

and then chuck it into Mathematica, it says:

$$i\sqrt{6}EllipticE[i,\frac{2}{3}]$$

The EllipticE[ , ] is a complete elliptic integral of the second kind.

In the words of Gandalf in the mines of moria (movie) "This foe is beyond any of you. Run!" (beyond me anyway, elliptic integrals, yick! :yuck: )

kevin