Evaluate the line integral

, where

is the parabola

in the plane

connecting the points

and

.

My method:

Okay, so it's probably good to start with a parameterisation:

where

.

I need to find

where

== Probably a typo: if must be

in the integral

For the first integral:

Let

=== This is wrong:

and not what you wrote

Tonio

So the two integrals are now:

For the second integral:

Let

Then, for the second integral, we have

Which becomes:

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???