Evaluate the line integral , where is the parabola in the plane connecting the points and .
Okay, so it's probably good to start with a parameterisation:
I need to find where
For the first integral:
So the two integrals are now:
For the second integral:
Then, for the second integral, we have
by FTC, the integral is
so substituting the limits gives:
So my overall answer to the question is:
Firstly, is this right? I have an in there that is undefined, but it removes itself quite nicely at the end.
Secondly, is there a faster way of doing this???