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):
But we also know that
So the integral for the x coordinate is:
....which I can't think of a way of integrating