It is mostly algebra lets focus on the radicand to start
Now if you take the square root we get
Now just integrate
You should be able to finish from here.
So, I am trying to find the length of a segment of a curve that is given by an x equation and a y equation and a limit placed on the 3rd variable t. Sorry in advance for the lack of actual images. Apparently I can't use that extension here? The initial problem is:
x = (e^t) + (e^-t) y = -2t + 5 0 <= t <= 3
Since the equation for finding the length of a curve segment described like this is: { [ (dx/dt)^2 ] + [ (dy/dt)^2 ] }^(1/2)
Using a pic from wolfram in the hopes of being a little clearer the formula is: http://www4a.wolframalpha.com/Calcul...=61&w=106&h=28
Then I calculate:
dx/dt = (e^t) - (e^-t)
dy/dt = -2t + 5
Which finally leads me to: { ( [ (e^t) - (e^-t) ]^2 ) + 4 }^(1/2) or http://www4a.wolframalpha.com/Calcul...=61&w=300&h=47
Now, I know that the answer is clearly in that last image but really I'm not so concerned with that as I am with the actual steps to solve this problem. By "problem" I am referring to that final integral calculation. I am led to believe that that is just true similar to how \int (1/x) = ln x. Even that equality can be stretched out to include some steps though if I remember correctly. I am looking for the steps required for this problem. Anyone?