Find the arc length of the parametric equation :
x= e^t , y= e^(-t) ,z= √2 t
0

Question

Find the arc length of the parametric equation :
x= e^t , y= e^(-t) ,z= √2 t
0<=t<=1

jamesj · Answer

So you want$$\int\limits_0^1 \sqrt{ (x')^2 + (y')^2 + (z')^2 } dt$$

anonymous · Answer

yes, but i can't solve the equation...........please help !!!!

jamesj · Answer

Now the expression in the integral isn't as bad as it seems once you evaluate it.  

Hint: cosh^2 t - sinh^2 t = 1

jamesj · Answer

and remember also that you can write
sinh t = 1/2(e^t - e^(-t))

anonymous · Answer

I'll try it out......thx for the hint !!

jamesj · Answer

sure.  I can tell you the answer, but I think you'll enjoy seeing how this works out.  It's quite elegant.

jamesj · Answer

Actually, you don't even need the hyperbolic functions if you can see the factorization, but I think it's helpful to know.

The other one for the record is: cosh t = (1/2)(e^t + e^(-t))

anonymous · Answer

I obtain sth like this : and I wonder if it's wrong..... :(
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