Have a problem that i have had a go at but am completely unsure if am anywhere near on the right track any help would be appreciated.
Evaluate the path integral;
Where f = xy;
And the path C is the part of the circle centred at the origin starting at (0,2) going anticlockwise ending at (-2,0).
I did that x=2cost, y=2sint;
so that c(t) = (2cost , 2sint),
where 0< t < pi/2
but am not sure i have set this up properly am a bit lost here.
Actually, I think the first problem is in the limits for t. As you go from (0,2) to (-2,0), that is, with , then .
Next , and , so .
And since this is the line integral of a scalar function, ds is the arc length parameter:
, so in terms of t,
and you have