I can't picture geometrically what this question is asking me to do.Let H be the curve parameterised by , and let L be the horizontal line from to .

Let be the vector field .

Question:Evaluate where is the closed curve formed by joining H and L (You may use either orientation of C).

Here's my attempt at a solution:

where and .

So I have to work out

=

From here is it okay to integrate each of the values with respect to ?

Here's what happens when I do (this is for the x coordinate. I thought it would be easier doing each one separately):

Let

This gives:

But we also know that

So the integral for the x coordinate is:

....which I can't think of a way of integrating