Hey bkbowser.
One suggestion is to try making the elements of the vector simple polynomials and then integrate the function that way (or use trig functions).
the given vector and the bounds of integration are;
differentiation gives;
definition of the length of a curve (were refers to the magnitude of the vector );
substituting the magnitude of and the bounds of integration into the equation;
So every problem, of this general form, so far has had a very simple integration where there is ultimately just a constant under the radical. So I think I'm looking for a way to combine the exponential functions into a constant and I can't come up with it so far.
If this is the wrong strategy please let me know.
I don't think we've discussed either of those methods in my program.
By trig functions do you mean the hyperbolic trig functions? We've been avoiding those sections in the text book and it's possible that this problem was assigned by mistake.
Is it possible to get more information on making the elements of the vector simple polynomials? Some keywords to look up on the internet perhaps?
If you just want practice for certain integrals, just either pick up a book or make your own up.
Personally I feel that once you get the hang of a few, you should just stop and move to the next thing.
Also if you are being tested exam wise on certain classes of integrals, focus on those since that is what you'll be marked on.
You are correct. I have copied the problem wrong.
So it should be
the given vector and the bounds of integration are;
differentiation gives;
definition of the length of a curve (were refers to the magnitude of the vector );
substituting the magnitude of and the bounds of integration into the equation;
I'm still stuck here. I've been trying to get the radicand to either look something like or get it to be a constant. I can't seem to do either here.
Should I be trying to substitute in some hyperbolic trig function in the first place?
I ask because we're not covering anything involving hyperbolic trig functions in my colleges program, so there's a chance I might not have to know how to do this problem at the moment!