Find Exact Arc Length of x=e^t + e^-t, y=5-2t, 0 ≤ x ≤ 3

[maff is tuff]

Homework Statement

Find the exact length of the curve x=e^t + e^-t , y=5-2t , 0≤ x≤ 3

Homework Equations

∫ √ ( (dx/dt)² + (dy/dt)² )dt

The Attempt at a Solution

My attempt at the solution is hopefully in the attachment. I could use Simpson's and get an approximate length but the directions say to find exact length. So did I mess up my algebra somewhere; I doubt it because this is one of several attempts and I keep getting stuck here. So does anyone know how to get me unstuck? Maybe a trick to make it more integrable? Sorry if I'm missing an obvious step that I can take, but as of now I don't see it. Thanks in advance for the help.

 

[jhae2.718]

These problems are often contrived so that you should be able to manipulate the terms under the square root into a perfect square.

Check your expansion of $$\left(e^t-e^{-t}\right)^2$$.

 

[maff is tuff]

Check your expansion of $$\left(e^t-e^{-t}\right)^2$$.

Yep that was it; my expansion was wrong. Thanks for the help :)

 

[jhae2.718]

No problem. :)